1. What is the Side Length Calculator?

Definition: This calculator finds the length of a side (a) in a right triangle using the hypotenuse (c) and an angle (θ).

Purpose: It helps students, engineers, and professionals quickly calculate triangle side lengths for geometry problems and real-world applications.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

Where:

• \( a \) — Opposite side length (meters)
• \( c \) — Hypotenuse length (meters)
• \( \theta \) — Angle opposite side a (degrees)

Explanation: The sine function relates the angle to the ratio of opposite side over hypotenuse in a right triangle.

3. Importance of Triangle Calculations

Details: Accurate side length calculations are essential in construction, navigation, physics, and engineering applications.

4. Using the Calculator

Tips: Enter the hypotenuse length and angle (must be between 0-90 degrees). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is 90 degrees?
A: At 90 degrees, side a equals the hypotenuse (sin(90°) = 1).

Q2: Can I use this for non-right triangles?
A: No, this formula specifically applies to right triangles. Use the Law of Sines for other triangles.

Q3: Why does my calculator give different results?
A: Ensure your calculator is in degree mode (not radians) when working with angles in degrees.

Q4: How accurate are the results?
A: Results are accurate to 3 decimal places. For higher precision, use more precise input values.

Q5: What if I know the adjacent side instead?
A: Use the cosine function instead: \( b = c \times \cos(\theta) \).