Triangle Trigonometry Calculator

Trigonometric Ratios:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

Angle (θ):

degrees

Opposite Side:

meters

Adjacent Side:

meters

Hypotenuse:

meters

Calculated Opposite Side:

Calculated Adjacent Side:

Calculated Hypotenuse:

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1. What is a Triangle Trigonometry Calculator?

Definition: This calculator computes trigonometric ratios (sine, cosine, tangent) and calculates missing sides of a right triangle when given an angle and at least one side length.

Purpose: It helps students, engineers, and professionals solve right triangle problems in mathematics, physics, and engineering applications.

2. How Does the Calculator Work?

The calculator uses the fundamental trigonometric ratios:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

Where:

\( \theta \) — Angle in degrees (must be between 0 and 90)
opposite — Side opposite to the angle θ
adjacent — Side adjacent to the angle θ
hypotenuse — Longest side of the right triangle

Explanation: The calculator can determine missing sides when given an angle and at least one side length, and can verify the consistency of provided values.

3. Importance of Trigonometry Calculations

Details: Right triangle trigonometry is fundamental in navigation, construction, physics, engineering, and computer graphics for calculating distances and angles.

4. Using the Calculator

Tips: Enter the angle (0-90 degrees) and at least one side length. The calculator will compute the missing sides. All lengths must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if I know two sides but not the angle?
A: Use inverse trigonometric functions (arcsin, arccos, arctan) which this calculator doesn't currently handle.

Q2: Does this work for non-right triangles?
A: No, these formulas only apply to right triangles. For other triangles, use the Law of Sines or Cosines.

Q3: What units should I use?
A: Any consistent units (meters, feet, etc.) can be used as long as all lengths are in the same unit.

Q4: Why is there an accuracy measurement?
A: If you provide two sides, it checks how closely they match the trigonometric ratios for the given angle.

Q5: What does a high accuracy value mean?
A: A high value (above 0.001) suggests your input values may not form a valid right triangle with the given angle.