Trigonometry of Right Triangles

Right Triangle Formulas:

\[ \sin(\theta) = \frac{opp}{hyp} \] \[ \cos(\theta) = \frac{adj}{hyp} \] \[ \tan(\theta) = \frac{opp}{adj} \]

Angle (θ):

degrees

Opposite Side:

meters

Adjacent Side:

meters

Hypotenuse:

meters

Opposite Side: meters

Adjacent Side: meters

Hypotenuse: meters

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1. What is Trigonometry of Right Triangles?

Definition: This calculator solves for unknown sides and angles in right triangles using trigonometric functions.

Purpose: It helps students, engineers, and professionals calculate missing dimensions in right-angled triangular shapes.

2. How Does the Calculator Work?

The calculator uses the fundamental trigonometric ratios:

\[ \sin(\theta) = \frac{opp}{hyp} \] \[ \cos(\theta) = \frac{adj}{hyp} \] \[ \tan(\theta) = \frac{opp}{adj} \]

Where:

\( \theta \) — Angle in degrees (between 0° and 90°)
\( opp \) — Length of side opposite to angle θ (meters)
\( adj \) — Length of side adjacent to angle θ (meters)
\( hyp \) — Length of the hypotenuse (meters)

Explanation: Enter any angle (θ) and any two sides, and the calculator will determine the remaining sides using trigonometric relationships.

3. Importance of Right Triangle Calculations

Details: Right triangle trigonometry is fundamental in construction, navigation, physics, and engineering for solving spatial problems.

4. Using the Calculator

Tips:

Enter the angle θ (must be between 0 and 90 degrees)
Enter any two known side lengths (leave others blank)
The calculator will compute all missing dimensions

5. Frequently Asked Questions (FAQ)

Q1: What if I only know one side length?
A: You need to know at least two elements (angle + one side, or two sides) to solve the triangle.

Q2: How accurate are the calculations?
A: Results are accurate to 3 decimal places, sufficient for most practical applications.

Q3: Can I use this for non-right triangles?
A: No, this calculator is specifically for right triangles. Use the Law of Sines/Cosines for other triangles.

Q4: What units should I use?
A: The calculator uses meters, but any consistent unit will work as long as all inputs use the same unit.

Q5: Why does the angle have to be between 0° and 90°?
A: Right triangles by definition have one 90° angle, so the other angles must each be less than 90°.