Right Triangle Calculator Sin Cos Tan

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

Angle θ:

Opposite Side:

Adjacent Side:

Hypotenuse:

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1. What is a Right Triangle Calculator?

Definition: This calculator solves for missing sides or angles in right triangles using trigonometric functions (sine, cosine, tangent).

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

2. How Does the Calculator Work?

The calculator uses these 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)
\( adj \) — Length of side adjacent to angle θ (meters)
\( hyp \) — Length of hypotenuse (meters)

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

3. Practical Applications

Details: Used in construction (roof pitch, ramps), engineering (force vectors), surveying, and physics problems.

4. Using the Calculator

Tips:

Enter angle in degrees (0-90)
Enter lengths in meters
Provide at least two values (angle + one side, or two sides)
Leave empty the values you want to calculate

5. Frequently Asked Questions (FAQ)

Q1: What if I know two sides but no angle?
A: The calculator will determine the angle using arctangent (if both legs) or arcsine/arccosine (if one leg and hypotenuse).

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

Q3: How accurate are the results?
A: Results are accurate to 3 decimal places for lengths and 2 decimal places for angles.

Q4: Can I use different units?
A: The calculator uses meters, but you can use any unit as long as you're consistent (all lengths in feet, cm, etc.).

Q5: What if I get an error message?
A: Ensure you've entered valid values (positive numbers, angle < 90°) and provided enough information (at least two values).