Calculate Length of Right Angle Triangle Side

Right Triangle Leg Formula:

\[ \text{leg} = \text{hyp} \times \sin(\theta) \]

Leg Length (meters):

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1. What is a Right Angle Triangle Side Calculator?

Definition: This calculator computes the length of a side (leg) in a right-angled triangle when you know the hypotenuse and one angle.

Purpose: It helps students, engineers, and construction professionals solve right triangle problems quickly and accurately.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

\[ \text{leg} = \text{hyp} \times \sin(\theta) \]

Where:

leg — Length of the side opposite to angle θ (meters)
hyp — Length of the hypotenuse (meters)
θ — Angle between hypotenuse and adjacent side (degrees)

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

3. Importance of Right Triangle Calculations

Details: Right triangle calculations are fundamental in geometry, physics, engineering, and construction for determining distances, slopes, and structural components.

4. Using the Calculator

Tips: Enter the hypotenuse length in meters and an angle between 0° and 90°. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a hypotenuse?
A: The hypotenuse is the longest side of a right triangle, opposite the right angle.

Q2: What angle range is valid?
A: The angle must be between 0° and 90° (exclusive) for a proper right triangle.

Q3: Can I calculate the other leg?
A: Yes, the adjacent leg can be found using cosine: adj = hyp × cos(θ).

Q4: What if I know two sides instead?
A: Use the Pythagorean theorem (a² + b² = c²) or inverse trigonometric functions.

Q5: How precise are the results?
A: Results are precise to 3 decimal places, sufficient for most practical applications.