Trigonometry Triangle Calculator Cos Tan Sin

Right Triangle Formulas:

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

Angle (θ):

degrees

Adjacent Side:

meters

Opposite Side:

meters

Hypotenuse:

meters

Calculated Adjacent Side:

Calculated Opposite Side:

Calculated Hypotenuse:

sin(θ):

cos(θ):

tan(θ):

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1. What is a Trigonometry Triangle Calculator?

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

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 ratios:

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

Where:

θ — Angle in degrees (must be between 0 and 90)
opp — Length of opposite side (meters)
adj — Length of adjacent side (meters)
hyp — Length of hypotenuse (meters)

Explanation: Enter any two known values (angle plus one side, or two sides) and the calculator will determine all other measurements.

3. Importance of Trigonometry Calculations

Details: Essential for construction, navigation, physics, engineering, and many STEM fields where angle and distance relationships are important.

4. Using the Calculator

Tips:

Enter the angle (must be between 0 and 90 degrees)
Enter any one or two side lengths
Leave unknown fields blank
The calculator will solve for all missing values

5. Frequently Asked Questions (FAQ)

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

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

Q3: How accurate are the results?
A: Results are accurate to 5 decimal places for trig functions and 3 decimal places for side lengths.

Q4: Can I use different units besides meters?
A: Yes, as long as you're consistent - all side lengths must use the same unit.

Q5: What if I get an error message?
A: Check that: (1) angle is between 0-90, (2) at least two values are provided, and (3) side lengths are positive numbers.