Right Angle Triangle Calculator Trig

Trigonometric Formulas:

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

Angle (θ):

degrees

Opposite Side:

meters

Hypotenuse:

meters

Adjacent Side:

meters

Calculated Opposite Side:

Calculated Hypotenuse:

Calculated Adjacent Side:

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1. What is a Right Angle Triangle Calculator?

Definition: This calculator solves for missing sides or angles in right-angled triangles using trigonometric functions.

Purpose: It helps students, engineers, and professionals quickly calculate triangle dimensions without manual trigonometric calculations.

2. How Does the Calculator Work?

The calculator uses the fundamental trigonometric formulas:

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

Where:

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

Explanation: Enter any two known values (angle + one side, or two sides) and the calculator will determine the remaining values.

3. Importance of Right Angle Triangle Calculations

Details: These calculations are fundamental in construction, navigation, physics, engineering, and many STEM fields.

4. Using the Calculator

Tips:

Enter the angle (θ) in degrees (0-90)
Enter any one side length to calculate the others
Or enter two sides to calculate the angle and third side
All lengths are in meters

5. Frequently Asked Questions (FAQ)

Q1: What's the minimum information needed?
A: You need either: (1) angle + one side, or (2) two sides to calculate the rest.

Q2: Why does the angle need to be between 0° and 90°?
A: This calculator is for right-angled triangles only, where one angle is exactly 90° and the others are acute (<90°).

Q3: How accurate are the results?
A: Results are accurate to 3 decimal places, sufficient for most practical applications.

Q4: Can I use different units?
A: The calculator uses meters, but you can use any consistent unit as long as all inputs use the same unit.

Q5: What if I get NaN or infinity as a result?
A: This means the inputs don't form a valid right-angled triangle. Check your values.