tan(θ) = opp/adj, Trig in right angled

Trigonometry in Right Angled Triangles

Trigonometric Formulas:

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

Angle (θ):

degrees

Opposite Side:

meters

Adjacent Side:

meters

Hypotenuse:

meters

Calculated Angle (θ): degrees

Calculated Opposite Side: meters

Calculated Adjacent Side: meters

Calculated Hypotenuse: meters

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1. What is Right Angle Trigonometry?

Definition: Trigonometric functions relate angles to side lengths in right-angled triangles.

Purpose: These calculations are fundamental in geometry, physics, engineering, and many practical applications like construction and navigation.

2. How Does the Calculator Work?

The calculator uses three primary trigonometric functions:

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

Where:

θ — 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 the hypotenuse (meters)

Explanation: Enter any two values to calculate the remaining sides and angle.

3. Importance of Right Angle Trigonometry

Details: Essential for calculating distances, heights, angles in construction, surveying, physics problems, and many real-world applications.

4. Using the Calculator

Tips:

Enter any two known values (angle + one side, or two sides)
Leave other fields empty for calculation
Angle must be between 0° and 90°
Side lengths must be positive values

5. Frequently Asked Questions (FAQ)

Q1: What if I know two sides but no angle?
A: The calculator will determine the angle using inverse tangent (if opp and adj are known) or inverse sine/cosine.

Q2: How precise are the calculations?
A: Results are accurate to 2 decimal places, suitable for most practical applications.

Q3: Can I use this for non-right triangles?
A: No, this calculator is specifically for right-angled triangles. Use the Law of Sines/Cosines for other triangles.

Q4: What units should I use?
A: The calculator uses meters for length, but any consistent unit will work (just be sure to interpret results accordingly).

Q5: Why does angle need to be between 0° and 90°?
A: Right triangles by definition have one 90° angle and two acute angles. Angles outside this range would not form a right triangle.