Similar Right Triangles
Similar Right Triangles Calculator
Find scale factor and missing matching sides in similar right triangles.
Calculator Mode
Find scale factor
Result
Formula:
Two right triangles are similar when they share the same angle measurements. Their sides may differ in length, but the ratios between corresponding sides are always equal. This constant ratio is called the scale factor.
This calculator helps you work with similar right triangles in three ways. You can find the scale factor between two triangles, calculate a missing side on the similar triangle, or reverse the process to find the original side. Each mode walks you through the formula step by step.
Choose a mode, enter the known values, and click Calculate. The calculator handles scale factor, missing similar side, and original side calculations.
Formula
Similar right triangles have equal angles, so every pair of matching sides shares the same ratio. If you know one pair of corresponding sides, you can find the scale factor k. Once you have k, you can calculate any missing side on either triangle.
The scale factor works in one direction. If k = 2, the similar triangle is twice as large. To go the other way, divide by k instead of multiplying. The formulas cover all three situations: finding k, finding a scaled side, and finding the original side.
Triangle Diagram
Triangle Diagram Key
- Both triangles have the same angle measures.
- Corresponding sides share the same ratio k.
- The smaller triangle is the original; the larger one is the similar triangle.
- If k is greater than 1, the similar triangle is larger. If k is less than 1, it is smaller.
- All three pairs of sides must have the same scale factor.
How to Use This Calculator
- Pick the mode that matches your problem: find k, find a similar side, or find an original side.
- Enter the known values in the input fields.
- Click Calculate to see the result with the formula applied.
- Switch modes using the tabs at the top if you need a different calculation.
- Click Reset to clear all fields.
Step-by-Step Examples
Example 1: Find the scale factor
Example 2: Find a missing similar side
Example 3: Find the original side
What the Result Means
The scale factor k tells you how many times larger or smaller the similar triangle is compared to the original. A scale factor of 2 means every side on the similar triangle is twice as long.
When you find a missing side, the result is the length of the corresponding side on the other triangle. This works because similar triangles maintain constant proportions across all pairs of matching sides.
Side Ratio
Similar right triangles keep the same matching-side ratios across both triangles.
If the scale factor is k, each side on the similar triangle equals its corresponding original side multiplied by k.
When to Use This Calculator
- Finding unknown side lengths in geometry problems involving similar triangles.
- Calculating dimensions for scale models or architectural drawings.
- Solving proportion problems on standardized math tests.
- Comparing shadow measurements to estimate the height of tall objects.
- Converting between blueprint measurements and actual building dimensions.
Common Mistakes
- Matching the wrong sides: always compare corresponding sides that are opposite the same angle.
- Using different scale factors for different side pairs: all pairs must share the same k.
- Dividing in the wrong direction: k equals similar side divided by original side, not the reverse.
- Assuming all right triangles are similar: two right triangles are only similar if they share a second angle.
- Forgetting that the right angle counts as a shared angle: if two right triangles have one more equal acute angle, they are similar.
FAQs
Answers to the most common right-triangle solving questions.
01 What makes two right triangles similar? expand_more
Two right triangles are similar when they have the same angle measures. Since both already have a 90-degree angle, they only need one more matching acute angle to be similar.
02 How do I find the scale factor between two similar right triangles? expand_more
Divide any side of the similar triangle by the corresponding side of the original triangle. The result is the scale factor k, and it should be the same for every pair of matching sides.
03 What does a scale factor of 1 mean? expand_more
A scale factor of 1 means the two triangles are the same size. Every corresponding side has equal length, making the triangles congruent.
04 Can the scale factor be a decimal? expand_more
Yes. A scale factor like 0.5 means the similar triangle is half the size of the original. Any positive number works as a scale factor.
05 Are all right triangles similar to each other? expand_more
No. Two right triangles are similar only if they share at least one acute angle in addition to the right angle. Different acute angles mean different proportions.
06 How do I find a missing side using the scale factor? expand_more
Multiply the corresponding original side by k to get the similar side. Or divide the similar side by k to find the original. The formula depends on which side you are solving for.