Similar Right Angle Triangle Calculator

Similar Right Angle Triangle Properties:

\[ \text{If } \angle A = \angle A' = 90^\circ \text{ and } \angle B = \angle B' \text{ then } \frac{AB}{A'B'} = \frac{BC}{B'C'} = \frac{AC}{A'C'} \]

Shared Angle:

degrees

Triangle 1 Side Length:

units

Corresponding Triangle 2 Side Length:

units

Unknown Side to Calculate:

Calculated Side Length:

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1. What Are Similar Right Angle Triangles?

Similar right angle triangles are triangles that each have a 90° angle and share an additional angle. These triangles have proportional sides and identical angle measurements, making them useful for various geometric calculations.

2. How Does the Calculator Work?

The calculator uses the properties of similar triangles:

\[ \frac{\text{Side}_1}{\text{Corresponding Side}_1} = \frac{\text{Side}_2}{\text{Corresponding Side}_2} = \text{Scale Factor} \]

Where:

Both triangles have a 90° angle
Both triangles share an additional angle
The third angle is automatically determined (90° - shared angle)
All corresponding sides are proportional

Explanation: Given three known values (shared angle and two corresponding sides), we can calculate any unknown side using the scale factor between the triangles.

3. Properties of Similar Right Triangles

Details: Similar right triangles maintain the same angles and have sides that are proportional. This relationship is fundamental in trigonometry and has practical applications in surveying, architecture, and physics.

4. Using the Calculator

Tips: Enter the shared angle (between 1-89 degrees), known side lengths from both triangles, and select which side you want to calculate. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why must the shared angle be less than 90 degrees?
A: Since both triangles already have a 90° angle, the shared angle must be between 1-89° to form a valid triangle (sum of angles = 180°).

Q2: Can I use this for triangles that aren't right triangles?
A: This calculator is specifically designed for right triangles. For other similar triangles, you would need different calculations.

Q3: What if I know different sides than the ones requested?
A: You need to provide corresponding sides from both triangles. If you have non-corresponding sides, you'll need to use trigonometric functions first.

Q4: How accurate are the results?
A: Results are mathematically precise based on the input values, rounded to 3 decimal places for readability.

Q5: Can this calculator find angles too?
A: This version calculates side lengths only. The angles are determined by the shared angle you provide and the right angle property.