Omni Calculator Trigonometry Triangle

Trigonometric Formulas:

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

Opposite Side (opp):

meters

Adjacent Side (adj):

meters

Hypotenuse (hyp):

meters

Angle (θ):

degrees

Calculated Opposite Side (opp):

Calculated Adjacent Side (adj):

Calculated Hypotenuse (hyp):

Calculated Angle (θ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is a Trigonometry Triangle Calculator?

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

Purpose: It helps students, engineers, and professionals quickly solve right triangle problems without manual calculations.

2. How Does the Calculator Work?

The calculator uses the fundamental trigonometric relationships:

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

Where:

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

Explanation: The calculator automatically determines which values can be calculated based on the inputs you provide.

3. Importance of Trigonometry in Triangles

Details: Right triangle trigonometry is fundamental in fields like architecture, engineering, physics, and navigation.

4. Using the Calculator

Tips: Enter any two of the four values (opposite, adjacent, hypotenuse, or angle) to calculate the remaining values. All lengths must be > 0 and angle between 0-90 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the sides?
A: The calculator works with any consistent unit (meters, feet, etc.). Just ensure all length inputs use the same unit.

Q2: Can I use this for non-right triangles?
A: No, this calculator is specifically for right triangles. For other triangles, you would need the Law of Sines or Cosines.

Q3: How precise are the results?
A: Results are calculated to high precision and displayed to 3 decimal places.

Q4: What if I get NaN or infinity as a result?
A: This means the inputs don't form a valid right triangle. Check your values and try again.

Q5: Can I calculate area with this tool?
A: Not directly, but once you have both legs (opposite and adjacent), area = (opp × adj)/2.