Solve the Right Triangle Calculator Trig

Side Formula:

\[ \text{side} = \text{hypotenuse} \times \sin(\theta) \]

Opposite Side (meters):

Adjacent Side (meters):

Remaining Angle (degrees):

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1. What is a Right Triangle Calculator?

Definition: This calculator solves for the unknown sides and angles of a right triangle when given the hypotenuse and one angle.

Purpose: It helps students, engineers, and professionals quickly solve right triangle problems using trigonometric functions.

2. How Does the Calculator Work?

The calculator uses trigonometric formulas:

\[ \text{opposite} = \text{hypotenuse} \times \sin(\theta) \] \[ \text{adjacent} = \text{hypotenuse} \times \cos(\theta) \] \[ \text{remaining angle} = 90^\circ - \theta \]

Where:

hypotenuse — Longest side of the right triangle
θ — Given angle (in degrees)
opposite — Side opposite to angle θ
adjacent — Side adjacent to angle θ

Explanation: The calculator converts the angle to radians, applies trigonometric functions, and calculates all missing components.

3. Importance of Right Triangle Calculations

Details: Right triangle trigonometry is fundamental in construction, navigation, physics, and engineering applications.

4. Using the Calculator

Tips: Enter the hypotenuse length (must be > 0) and one angle (must be between 0° and 90°). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What if I know two sides instead?
A: Use the Pythagorean theorem (a² + b² = c²) for sides, then inverse trig functions for angles.

Q2: Does the calculator work for non-right triangles?
A: No, this calculator is specifically for right triangles (90° angle).

Q3: How precise are the results?
A: Results are precise to 3 decimal places for sides and 1 decimal place for angles.

Q4: Can I use this for radians instead of degrees?
A: The calculator currently only accepts degrees, but converts them internally to radians.

Q5: What's the relationship between the sides?
A: The hypotenuse is always the longest side, opposite to the right angle.