How to Solve a Right Triangle: Complete Guide & Formulas

Welcome to the definitive guide on solving right triangles. Whether you are a student preparing for a geometry exam, a DIY homeowner calculating roof pitch, or an engineer designing a bridge, mastering right triangles is an essential skill.

Solving a right triangle means finding all of its missing side lengths and angle measures based on the information you already have. In this comprehensive guide, we will break down every method step-by-step, starting from the basics and moving to real-world applications.

After reading this guide you will be able to:

• Find missing sides
• Find missing angles
• Use the Pythagorean Theorem
• Use SOHCAHTOA
• Solve real-world problems
• Check your answers

Table of Contents

1. What Does It Mean to Solve a Right Triangle?
2. Parts of a Right Triangle
3. Information Needed Before Solving
4. Method 1: Solve Using the Pythagorean Theorem
5. Method 2: Solve Using SOHCAHTOA
6. Method 3: Using Inverse Trigonometric Functions
7. Method 4: Using Special Right Triangles
8. Method 5: Coordinate Geometry
9. Complete Worked Examples
10. Real-Life Applications
11. Common Mistakes
12. Practice Problems
13. Frequently Asked Questions
14. Summary

What Does It Mean to Solve a Right Triangle?

To solve a right triangle means to calculate the exact lengths of all three sides and the measurements of all three angles. Every right triangle has six parts (three sides and three angles), and you can find all of them if you know just two specific values (plus the 90-degree angle).

The ultimate goal is a complete mathematical picture of the shape. Because we already know one angle is exactly 90 degrees, we only need to find the remaining two acute angles and the three side lengths.

Comparison Table: Known vs. Unknown Values

Parts of a Right Triangle

A right triangle has three sides: the hypotenuse, the opposite side, and the adjacent side, along with one 90-degree angle and two acute angles. Identifying these parts correctly is the crucial first step before doing any math.

• Hypotenuse: The longest side of the triangle, always located directly across from the 90-degree right angle.
• Right Angle: The 90-degree corner, usually marked with a small square.
• Acute Angles: The two remaining angles. Their sum is always exactly 90 degrees (meaning they are complementary).
• Legs: The two shorter sides that form the right angle. When referencing a specific acute angle, these legs are called the opposite and adjacent sides.
• Opposite Side: The leg directly across from the angle you are focusing on.
• Adjacent Side: The leg that forms the angle you are focusing on (along with the hypotenuse).
• Altitude: A line from a vertex perpendicular to the opposite side.
• Median: A line from a vertex to the midpoint of the opposite side.

Comparison Table: Triangle Parts

Information Needed Before Solving

You can solve any right triangle as long as you know the 90-degree angle and at least two other specific pieces of information, one of which must be a side length.

Case 1: Two sides are known

Use the Pythagorean Theorem to find the third side. Use inverse trigonometry to find the acute angles.

Case 2: One side and one angle

Use SOHCAHTOA (sine, cosine, or tangent) to find another side. Subtract the known angle from 90° to find the third angle.

Case 3: Hypotenuse and one side

Use the Pythagorean Theorem to find the missing leg. Use inverse sine or inverse cosine to find the angles.

Case 4: Area is known

If you know the area and one leg, use the area formula (Area = 1/2 * base * height) to find the other leg. Then proceed to Case 1.

Case 5: Coordinates are known

If you have the (x,y) coordinates of the vertices, use the distance formula to find the lengths of the sides, then proceed to Case 1.

Case 6: Special triangles

If the angles are 30-60-90 or 45-45-90, you only need one side to find all other sides using fixed ratios, skipping complex formulas.

Decision Table: Which Formula to Use?

Method 1: Solve Using the Pythagorean Theorem

The Pythagorean Theorem formula is a² + b² = c², where ‘a’ and ‘b’ are the legs, and ‘c’ is the hypotenuse. It is used to find a missing third side when the other two sides are known.

When to Use

Use this formula strictly when you know two sides of a right triangle and need the third.

When NOT to Use

Do not use this if you only know one side length, or if the triangle is not a right triangle.

Advantages & Limitations

It is universally accurate for right triangles and easy to calculate. However, it cannot find missing angles.

10 Solved Examples

1. Given: a=3, b=4. Solve: 3² + 4² = c² ➔ 9 + 16 = c² ➔ 25 = c² ➔ c=5.
2. Given: a=5, b=12. Solve: 5² + 12² = c² ➔ 25 + 144 = c² ➔ 169 = c² ➔ c=13.
3. Given: a=8, b=15. Solve: 8² + 15² = c² ➔ 64 + 225 = c² ➔ 289 = c² ➔ c=17.
4. Given: a=7, b=24. Solve: 7² + 24² = c² ➔ 49 + 576 = c² ➔ 625 = c² ➔ c=25.
5. Given: a=9, b=40. Solve: 9² + 40² = c² ➔ 81 + 1600 = c² ➔ 1681 = c² ➔ c=41.
6. Given: c=10, a=6. Solve: 6² + b² = 10² ➔ 36 + b² = 100 ➔ b² = 64 ➔ b=8.
7. Given: c=26, a=10. Solve: 10² + b² = 26² ➔ 100 + b² = 676 ➔ b² = 576 ➔ b=24.
8. Given: c=15, b=9. Solve: a² + 9² = 15² ➔ a² + 81 = 225 ➔ a² = 144 ➔ a=12.
9. Given: c=34, a=16. Solve: 16² + b² = 34² ➔ 256 + b² = 1156 ➔ b² = 900 ➔ b=30.
10. Given: a=1, b=1. Solve: 1² + 1² = c² ➔ 1 + 1 = c² ➔ c=√2 ≈ 1.414.

Method 2: Solve Using SOHCAHTOA

SOHCAHTOA is an acronym used to remember the three main trigonometric functions: Sine (Opposite/Hypotenuse), Cosine (Adjacent/Hypotenuse), and Tangent (Opposite/Adjacent). Use it to find a missing side when you have one angle and one side.

Sine (SOH)

sin(θ) = Opposite / Hypotenuse. Use when the problem involves the opposite side and the hypotenuse.

Cosine (CAH)

cos(θ) = Adjacent / Hypotenuse. Use when the problem involves the adjacent side and the hypotenuse.

Tangent (TOA)

tan(θ) = Opposite / Adjacent. Use when the problem involves the opposite and adjacent sides, without the hypotenuse.

SOHCAHTOA Decision Tree

• Do you know/need the Hypotenuse?
  • YES: Do you know/need the Opposite side? ➔ Use Sine
  • YES: Do you know/need the Adjacent side? ➔ Use Cosine
  • NO: ➔ Use Tangent

10 Solved Examples (SOHCAHTOA)

1. Given: Angle=30°, Hypotenuse=10. Find Opposite. Solve: sin(30°) = Opp/10 ➔ 0.5 = Opp/10 ➔ Opp = 5.
2. Given: Angle=60°, Hypotenuse=20. Find Adjacent. Solve: cos(60°) = Adj/20 ➔ 0.5 = Adj/20 ➔ Adj = 10.
3. Given: Angle=45°, Adjacent=7. Find Opposite. Solve: tan(45°) = Opp/7 ➔ 1 = Opp/7 ➔ Opp = 7.
4. Given: Angle=25°, Opposite=4. Find Hypotenuse. Solve: sin(25°) = 4/Hyp ➔ 0.4226 = 4/Hyp ➔ Hyp = 4 / 0.4226 ≈ 9.46.
5. Given: Angle=50°, Adjacent=12. Find Hypotenuse. Solve: cos(50°) = 12/Hyp ➔ 0.6428 = 12/Hyp ➔ Hyp = 12 / 0.6428 ≈ 18.67.
6. Given: Angle=35°, Opposite=8. Find Adjacent. Solve: tan(35°) = 8/Adj ➔ 0.7002 = 8/Adj ➔ Adj = 8 / 0.7002 ≈ 11.43.
7. Given: Angle=15°, Hypotenuse=50. Find Opposite. Solve: sin(15°) = Opp/50 ➔ 0.2588 = Opp/50 ➔ Opp ≈ 12.94.
8. Given: Angle=75°, Hypotenuse=100. Find Adjacent. Solve: cos(75°) = Adj/100 ➔ 0.2588 = Adj/100 ➔ Adj ≈ 25.88.
9. Given: Angle=80°, Adjacent=5. Find Opposite. Solve: tan(80°) = Opp/5 ➔ 5.6713 = Opp/5 ➔ Opp ≈ 28.36.
10. Given: Angle=40°, Opposite=10. Find Adjacent. Solve: tan(40°) = 10/Adj ➔ 0.8391 = 10/Adj ➔ Adj = 10 / 0.8391 ≈ 11.92.

Method 3: Using Inverse Trigonometric Functions

Inverse trigonometric functions (arcsin, arccos, arctan) are used to find a missing angle when you already know two side lengths of a right triangle.

• Inverse Sine (sin⁻¹): Angle = sin⁻¹(Opposite / Hypotenuse)
• Inverse Cosine (cos⁻¹): Angle = cos⁻¹(Adjacent / Hypotenuse)
• Inverse Tangent (tan⁻¹): Angle = tan⁻¹(Opposite / Adjacent)

Examples

1. Given: Opp=3, Hyp=5. Find Angle: sin⁻¹(3/5) = sin⁻¹(0.6) ≈ 36.87°.
2. Given: Adj=4, Hyp=5. Find Angle: cos⁻¹(4/5) = cos⁻¹(0.8) ≈ 36.87°.
3. Given: Opp=5, Adj=12. Find Angle: tan⁻¹(5/12) ≈ 22.62°.
4. Given: Opp=1, Hyp=2. Find Angle: sin⁻¹(1/2) = 30°.
5. Given: Opp=1, Adj=1. Find Angle: tan⁻¹(1) = 45°.

Calculator Tip: Ensure your calculator is set to ‘Degrees’ mode unless the problem specifically asks for ‘Radians’.

Method 4: Using Special Right Triangles

Special right triangles have set angle proportions that allow you to solve for sides without trigonometry. The two types are 30-60-90 and 45-45-90 triangles.

30-60-90 Triangle

The ratio of the sides opposite the 30°, 60°, and 90° angles is x : x√3 : 2x.

• Short leg (opposite 30°): x
• Long leg (opposite 60°): x√3
• Hypotenuse (opposite 90°): 2x

45-45-90 Triangle (Isosceles Right Triangle)

The ratio of the sides opposite the 45°, 45°, and 90° angles is x : x : x√2.

• Leg 1: x
• Leg 2: x
• Hypotenuse: x√2

Worked Examples

1. 30-60-90: Short leg = 5. Find Hypotenuse. (5 * 2 = 10).
2. 30-60-90: Hypotenuse = 20. Find Short leg. (20 / 2 = 10).
3. 30-60-90: Short leg = 4. Find Long leg. (4 * √3 = 4√3).
4. 45-45-90: Leg = 6. Find Hypotenuse. (6 * √2 = 6√2).
5. 45-45-90: Hypotenuse = 10. Find Leg. (10 / √2 = 5√2).

Method 5: Coordinate Geometry

In coordinate geometry, you use the distance formula to calculate the lengths of a right triangle’s sides based on the (x, y) coordinates of its vertices.

Distance Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

By finding the length of the horizontal leg and the vertical leg on a graph, you can then apply the Pythagorean Theorem to find the hypotenuse.

Example

Vertices: A(1, 1), B(4, 1), C(1, 5)

1. Find base AB: √( (4-1)² + (1-1)² ) = √(3² + 0) = 3.
2. Find height AC: √( (1-1)² + (5-1)² ) = √(0 + 4²) = 4.
3. Find Hypotenuse BC: a² + b² = c² ➔ 3² + 4² = c² ➔ c=5.

Complete Worked Examples

Solving real math problems requires putting all these concepts together. Below are 30 complete, step-by-step examples across various difficulty levels and real-world scenarios.

Easy Examples (1-5)

1. Problem: Legs are 6 and 8. Find hypotenuse.
   • Formula: a² + b² = c²
   • Calculation: 6² + 8² = 36 + 64 = 100. √100 = 10.
   • Answer: 10
2. Problem: Hypotenuse is 13, leg is 5. Find the other leg.
   • Calculation: 13² - 5² = 169 - 25 = 144. √144 = 12.
   • Answer: 12
3. Problem: One angle is 40°. Find the other acute angle.
   • Calculation: 90 - 40 = 50.
   • Answer: 50°
4. Problem: Leg is 7, adjacent angle is 45°. Find the other leg.
   • Calculation: It’s a 45-45-90 triangle. Legs are equal.
   • Answer: 7
5. Problem: Opp=10, Adj=10. Find the angle.
   • Calculation: tan⁻¹(10/10) = tan⁻¹(1) = 45°.
   • Answer: 45°

Intermediate Examples (6-15)

6. Problem: Hyp=20, angle=30°. Find opposite side.
   • Formula: sin(θ) = Opp/Hyp
   • Calculation: sin(30°) = Opp/20 ➔ 0.5 * 20 = 10.
   • Answer: 10
7. Problem: Adj=15, angle=60°. Find hypotenuse.
   • Calculation: cos(60°) = 15/Hyp ➔ Hyp = 15 / 0.5 = 30.
   • Answer: 30
8. Problem: Opp=12, angle=22°. Find adjacent.
   • Calculation: tan(22°) = 12/Adj ➔ Adj = 12 / 0.404 = 29.7.
   • Answer: 29.7
9. Problem: Hyp=50, Opp=25. Find the angle.
   • Calculation: sin⁻¹(25/50) = sin⁻¹(0.5) = 30°.
   • Answer: 30°
10. Problem: Adj=8, Hyp=11. Find the angle.
    • Calculation: cos⁻¹(8/11) = cos⁻¹(0.727) ≈ 43.3°.
    • Answer: 43.3°
11. Problem: Opp=9, Adj=14. Find hypotenuse.
    • Calculation: 9² + 14² = 81 + 196 = 277. √277 ≈ 16.64.
    • Answer: 16.64
12. Problem: Right triangle area is 24, base is 6. Find hypotenuse.
    • Calculation: Area = 0.5 * b * h ➔ 24 = 0.5 * 6 * h ➔ h = 8. Legs are 6, 8. Hyp = √(6²+8²) = 10.
    • Answer: 10
13. Problem: Equilateral triangle with side 10. Drop an altitude to form a right triangle. Find altitude.
    • Calculation: Base becomes 5. Hyp is 10. Alt = √(10² - 5²) = √75 = 5√3.
    • Answer: 5√3 ≈ 8.66
14. Problem: Diagonal of a square is 14. Find the side length.
    • Calculation: x² + x² = 14² ➔ 2x² = 196 ➔ x² = 98 ➔ x = √98 = 7√2.
    • Answer: 7√2 ≈ 9.9
15. Problem: A 30-60-90 triangle has a long leg of 9. Find the short leg.
    • Calculation: Long = Short * √3 ➔ 9 = x√3 ➔ x = 9/√3 = 3√3.
    • Answer: 3√3 ≈ 5.2

Advanced & Real-World Examples (16-30)

16. Construction (Ladder): A 20ft ladder leans against a wall, base is 5ft away. How high does it reach?
    • Calculation: 20² - 5² = 400 - 25 = 375. √375 ≈ 19.36 ft.
17. Architecture (Roof Pitch): A roof rises 6ft over a 12ft horizontal run. What is the angle of elevation?
    • Calculation: tan⁻¹(6/12) = tan⁻¹(0.5) ≈ 26.56°.
18. Surveying: A surveyor stands 100m from a building, measures angle to top as 40°. Height?
    • Calculation: tan(40°) = Height/100 ➔ Height = 100 * 0.839 = 83.9m.
19. Aviation: A plane takes off at a 15° angle. How far has it traveled horizontally when altitude is 5000ft?
    • Calculation: tan(15°) = 5000/Adj ➔ Adj = 5000 / 0.2679 ≈ 18,663 ft.
20. Navigation: A boat travels 30 miles North, then 40 miles East. How far from start?
    • Calculation: 30² + 40² = 900 + 1600 = 2500. √2500 = 50 miles.
21. Physics: A force vector has x-component 40N, y-component 30N. Resultant force?
    • Calculation: √(40² + 30²) = √2500 = 50N.
22. Wheelchair Ramp: Ramp must rise 2ft. Angle cannot exceed 4.76°. Minimum ramp length (hypotenuse)?
    • Calculation: sin(4.76°) = 2/Hyp ➔ Hyp = 2 / 0.083 ≈ 24.1 ft.
23. Computer Graphics: Ray cast from (0,0) hits (8,15). Distance?
    • Calculation: √(8² + 15²) = √289 = 17.
24. Astronomy: Star parallax angle is 0.5 arcsec. Base is 1 AU. (Simplified): tan(0.5”) = 1/Dist.
    • Calculation: Dist = 1 / tan(0.5”) = extremely large distance in AU (approx 206,265 AU = 1 parsec).
25. Engineering (Guy Wire): Antenna is 50m tall. Wire anchored 20m from base. Wire length?
    • Calculation: √(50² + 20²) = √(2500+400) = √2900 ≈ 53.85m.
26. Road Construction: A road grade is 8% (rise 8, run 100). What is the angle?
    • Calculation: tan⁻¹(8/100) = tan⁻¹(0.08) ≈ 4.57°.
27. Bridge Design: Truss diagonal connects a 3m wide, 4m tall rectangular section. Length?
    • Calculation: √(3² + 4²) = 5m.
28. Machine Design: A wedge has an angle of 10° and a base of 5cm. Thickness (opposite)?
    • Calculation: tan(10°) = Opp/5 ➔ Opp = 5 * 0.1763 = 0.88cm.
29. Robotics: A robot arm extends 10cm on X axis, 10cm on Y axis. Joint angle to reach point?
    • Calculation: tan⁻¹(10/10) = 45°.
30. Shadow Calculation: A 6ft man casts an 8ft shadow. Sun angle?
    • Calculation: tan⁻¹(6/8) = tan⁻¹(0.75) ≈ 36.87°.

Real-Life Applications

Right triangles are the foundation of applied geometry. Here is how they are used across different industries.

Construction & Architecture

Builders use the 3-4-5 rule (a Pythagorean triple) to ensure corners are perfectly square (90 degrees). Architects use right triangle trigonometry to calculate the pitch of a roof and ensure stairs meet building code safety angles.

Engineering & Surveying

Civil engineers calculate load-bearing angles on bridge trusses. Land surveyors use total stations to measure angles and use right triangles to calculate distances across impassable terrain, like rivers.

Navigation & Aviation

GPS systems triangulate positions using complex geometry derived from right triangles. Pilots use trigonometry to calculate crosswind correction angles and rates of descent.

Computer Graphics & Video Games

Every 3D environment in a video game is rendered using millions of tiny triangles. Graphic engines use right triangle math to calculate lighting angles, physics collisions, and rendering distances.

Common Mistakes

Here are 25 common mistakes students make, why they happen, and how to avoid them.

1. Using Pythagorean theorem on non-right triangles: Assuming a² + b² = c² works on all triangles. Correction: It only works if there is a 90° angle.
2. Confusing Opposite and Adjacent: Correction: The opposite side does not touch the angle; the adjacent side forms the angle.
3. Calculator in Radians mode: Getting negative or decimal answers for basic degree problems. Correction: Switch to ‘Degree’ mode.
4. Adding instead of subtracting (Pythagoras): Finding a leg using c² + b² = a². Correction: Subtract the square of the known leg from the hypotenuse squared: c² - b² = a².
5. Forgetting to take the square root: Ending with c² = 25 and saying the side is 25. Correction: c = √25 = 5.
6. Using regular Sine instead of Inverse Sine: Trying to find an angle with sin(x) instead of sin⁻¹(x).
7. Mixing up Sine and Cosine: Correction: Remember SOH CAH TOA.
8. Misidentifying the Hypotenuse: Thinking the longest side is just the one drawn vertically. Correction: It is always strictly opposite the 90° angle.
9. Assuming a 3-4-5 triangle when sides are 3 and 5: If 5 is a leg, the hypotenuse is √(9+25) = √34, not 4.
10. Rounding too early: Rounding numbers in the middle of a calculation introduces massive errors later. Correction: Keep decimals until the final answer.
11. Assuming angles are 45° just because it looks like it: Correction: Never trust a drawing; trust the math.
12. Using TOA for the hypotenuse: Tangent does not involve the hypotenuse.
13. Forgetting that the two acute angles sum to 90°: Correction: If one is 30°, the other is 60°.
14. Applying 30-60-90 rules to any triangle: Correction: Only works if angles are exactly 30°, 60°, 90°.
15. Misplacing the decimal point in trig ratios.
16. Putting the adjacent side over the opposite for Tangent: Correction: It is Opp/Adj.
17. Square rooting individual terms: √a² + √b² = √c². Correction: This is mathematically illegal. Evaluate (a²+b²) first.
18. Using inverse trig to find a side length: Inverse trig only outputs angles.
19. Mixing units: One side is inches, the other is feet. Correction: Convert to the same unit first.
20. Assuming the altitude always bisects the base: Correction: Only true in isosceles right triangles.
21. Calculating area incorrectly: Using the hypotenuse as the height. Correction: Area = 0.5 * leg1 * leg2.
22. Using the wrong formula to check work: If you used Pythagoras, check with trig, not Pythagoras again.
23. Typing fractions wrong in the calculator: Correction: Use parentheses, e.g., sin⁻¹(3/4).
24. Forgetting the units in the final answer.
25. Writing the final angle over 90°: Acute angles in a right triangle must be less than 90°.

Practice Problems

Test your knowledge with these 40 practice questions. (Answers provided below).

Beginner (1-15: Find the missing side using Pythagoras)

1. a=6, b=8, c=?
2. a=5, b=12, c=?
3. a=9, b=12, c=?
4. a=8, b=15, c=?
5. c=13, a=5, b=?
6. c=25, a=7, b=?
7. c=10, b=6, a=?
8. c=17, a=8, b=?
9. a=1, b=1, c=?
10. a=2, b=3, c=?
11. a=4, b=4, c=?
12. c=20, a=12, b=?
13. c=15, b=9, a=?
14. a=10, b=24, c=?
15. a=14, b=48, c=?

Intermediate (16-25: Basic SOHCAHTOA) 16. angle=30°, hyp=10, opp=? 17. angle=45°, adj=5, opp=? 18. angle=60°, hyp=8, adj=? 19. angle=20°, opp=4, hyp=? 20. angle=70°, adj=10, hyp=? 21. opp=3, hyp=5, angle=? 22. adj=4, hyp=5, angle=? 23. opp=5, adj=12, angle=? 24. opp=7, hyp=25, angle=? 25. adj=8, hyp=17, angle=?

Advanced (26-40: Mixed Applications) 26. A ladder 15m long hits a wall 12m high. Base distance? 27. 30-60-90 triangle, short leg=7. Hypotenuse? 28. 45-45-90 triangle, leg=9. Hypotenuse? 29. Area=30, base=5. Hypotenuse? 30. Rectangle 6x8. Length of diagonal? 31. angle=15°, opp=10. Adjacent? 32. angle=85°, adj=2. Opposite? 33. Isosceles right triangle hyp=10. Leg? 34. Equilateral triangle side=6. Altitude? 35. Distance from (0,0) to (5,12)? 36. Distance from (1,1) to (4,5)? 37. Ship sails 50 miles North, 120 miles East. Direct distance? 38. Plane descends 3 miles over 40 miles ground. Hypotenuse distance? 39. Roof pitch angle if rise is 4, run is 12? 40. Triangle side a=20, b=21, find c.

Solutions Checklist (Briefly):

1. 10 | 2. 13 | 3. 15 | 4. 17 | 5. 12 | 6. 24 | 7. 8 | 8. 15 | 9. √2 | 10. √13 | 11. 4√2 | 12. 16 | 13. 12 | 14. 26 | 15. 50
2. 5 | 17. 5 | 18. 4 | 19. 11.7 | 20. 29.2 | 21. 36.9° | 22. 36.9° | 23. 22.6° | 24. 16.3° | 25. 61.9°
3. 9m | 27. 14 | 28. 9√2 | 29. 13 | 30. 10 | 31. 37.3 | 32. 22.8 | 33. 5√2 | 34. 3√3 | 35. 13 | 36. 5 | 37. 130 | 38. 40.11 | 39. 18.4° | 40. 29

Related Right Triangle Calculators

To make solving right triangles as easy as possible, we have built a suite of free, highly accurate calculators tailored to every specific problem type. Check them out below:

General Triangles & Sides

• Ultimate Right Triangle Solver
• Missing Side Calculator
• Missing Leg Calculator (from Hypotenuse & Leg)
• Hypotenuse Calculator
• Pythagorean Theorem Calculator
• Pythagorean Triples Calculator
• Similar Right Triangles Calculator

Angles & Trigonometry

• Missing Angle Calculator
• Sine Ratio Calculator
• Cosine Ratio Calculator
• Tangent Ratio Calculator
• Angle from Sine Calculator
• Angle from Cosine Calculator
• Angle from Tangent Calculator

Area, Perimeter & Advanced Properties

• Right Triangle Area Calculator
• Right Triangle Perimeter Calculator
• Right Triangle Semiperimeter Calculator
• Right Triangle Altitude Calculator
• Right Triangle Inradius Calculator
• Right Triangle Circumradius Calculator

Special Right Triangles

• 45-45-90 Triangle Calculator
• 30-60-90 Triangle Calculator
• 3-4-5 Triangle Calculator
• 5-12-13 Triangle Calculator