Side Calculations
Right Triangle Side From Cosine Calculator
Use this calculator to find adjacent side b from angle A and hypotenuse c.
Leg b from Cosine Calculator
This calculator finds Adjacent side b using .
Enter inputs to calculate Adjacent side b.
Adjacent side b
Result-
Solution Steps
Formula:
What This Tool Solves
This calculator takes angle A and hypotenuse c as inputs and returns the adjacent side b. Cosine is the ratio that links these three values, so the formula needs no rearranging.
Known values
Angle A and hypotenuse c
Finds
Adjacent side b
Main formula
b = c × cos(A)
Best for
Finding horizontal run, base distance, or ground projection
Right Triangle Diagram: Side b from Cosine
In this layout, angle A is at the bottom-right. The adjacent side b runs along the base, sitting right next to angle A. The hypotenuse c stretches from angle A up to the top vertex. The calculator uses these two known values to find b.
Diagram Key
Opposite side a is directly across from angle A. It is not needed for this calculation.
Adjacent side b runs along the base next to angle A. This is the value the calculator returns.
Hypotenuse c is the longest side, opposite the right angle. You provide this as input.
- For angle A, side a is opposite, side b is adjacent, and side c is the hypotenuse.
- The adjacent side is always the side that touches angle A and the right angle.
- The result b will always be shorter than c.
Side From Cosine Formula
The cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse. Written as a ratio: cos(A) = b / c. Multiplying both sides by c gives the direct formula below.
Here, c is the hypotenuse (the longest side, opposite the 90-degree angle), A is the acute angle, and b is the adjacent side you want. The cosine function converts the angle into the exact fraction of the hypotenuse that equals the adjacent side.
How to Use This Calculator
- Find the hypotenuse c in your right triangle. It is the side across from the right angle and always the longest side.
- Identify your known acute angle A. Confirm the value is in degrees.
- Type the hypotenuse c into the first field.
- Type angle A into the second field.
- Press Calculate to see the adjacent side b and the step-by-step solution.
Step-by-Step Example: Find Adjacent Side b
Given: A = 36.87 degrees, c = 5. Find adjacent side b using the cosine formula.
What the Result Means
The output labeled Adjacent side b is the side that sits next to angle A and also touches the right angle. In real-world problems, this is often the horizontal distance, ground run, or base measurement.
Like the opposite side, the adjacent side is always shorter than the hypotenuse. If the angle is small, b will be close to c. If the angle is large (near 90 degrees), b shrinks toward zero.
When to Use This Calculator
Choose this tool when you have the hypotenuse and an angle and need the horizontal or base component. This pattern appears in slope calculations, shadow problems, and structural layout tasks.
It pairs naturally with the sine calculator. Together, they let you split the hypotenuse into its opposite and adjacent components from the same angle.
Common situations:
- Finding the horizontal distance a ladder covers on the ground from ladder length and angle.
- Calculating the ground run of a ramp when the ramp length and angle are known.
- Determining the shadow length cast by a pole when the sun angle and pole-to-tip distance are given.
- Breaking a force vector into its horizontal component in physics problems.
Common Mistakes
The most frequent error is mixing up which trig function to use. Sine and cosine both use the hypotenuse, but they return different sides. Cosine gives the adjacent side, sine gives the opposite.
Watch out for:
- Using sine instead of cosine. Sine returns the opposite side, not the adjacent.
- Entering the opposite side instead of the hypotenuse.
- Confusing side b with side a. Side b is adjacent to angle A, side a is opposite.
- Forgetting that c is the hypotenuse and never side a or side b.
- Using an angle in radians when the calculator expects degrees.
Related Calculators
Frequently Asked Questions
Answers to the most common right-triangle solving questions.
01 What does b = c × cos(A) calculate? expand_more
It calculates the adjacent side b of a right triangle when you know the hypotenuse c and an acute angle A. The cosine function converts the angle into the correct ratio.
02 How is this different from the sine calculator? expand_more
The sine calculator finds the opposite side a. This cosine calculator finds the adjacent side b. Both use the hypotenuse, but they return different sides of the triangle.
03 What does adjacent side mean? expand_more
The adjacent side is the side that touches the angle you are using and also touches the right angle. For angle A, the adjacent side is b.
04 Can b be larger than the hypotenuse? expand_more
No. In a right triangle, both non-hypotenuse sides are always shorter than the hypotenuse. If your result is larger than c, check your inputs.
05 What happens if I enter a very small angle? expand_more
As angle A gets closer to 0 degrees, cos(A) approaches 1, so b gets closer to c. The adjacent side is nearly the full length of the hypotenuse at very small angles.