Special Right Triangle Calculator Symbolab

45-45-90 Triangle Formula:

\[ \text{side} = \frac{\text{hypotenuse}}{\sqrt{2}} \]

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1. What Are Special Right Triangles?

Special right triangles are triangles with fixed angle measures and consistent side length ratios. The two most common are the 45-45-90 and 30-60-90 triangles, which have predictable relationships between their sides.

2. How Does the Calculator Work?

For 45-45-90 triangles:

\[ \text{side} = \frac{\text{hypotenuse}}{\sqrt{2}} \] \[ \text{hypotenuse} = \text{side} \times \sqrt{2} \]

For 30-60-90 triangles:

\[ \text{short side} = \frac{\text{hypotenuse}}{2} \] \[ \text{long side} = \text{short side} \times \sqrt{3} \]

3. Importance of Special Right Triangles

Details: These triangles are fundamental in geometry, trigonometry, and many practical applications like construction and engineering. Their predictable ratios allow for quick calculations without advanced trigonometry.

4. Using the Calculator

Tips: Select the triangle type, enter the known length, specify whether it's a side or hypotenuse, and click calculate. The calculator will determine all other side lengths.

5. Frequently Asked Questions (FAQ)

Q1: What are the angle measures in special right triangles?
A: 45-45-90 has angles of 45°, 45°, and 90°. 30-60-90 has angles of 30°, 60°, and 90°.

Q2: What are the side ratios for 45-45-90?
A: The sides are in the ratio 1:1:√2 (leg:leg:hypotenuse).

Q3: What are the side ratios for 30-60-90?
A: The sides are in the ratio 1:√3:2 (short leg:long leg:hypotenuse).

Q4: Can these formulas be used for any right triangle?
A: No, only for the specific angle combinations of 45-45-90 or 30-60-90.

Q5: How accurate are the calculations?
A: The calculations are mathematically precise based on the input values.