Trigonometry Right Angle Triangle Calculator

Right Angle Triangle Formulas:

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

Opposite Side (meters):

Calculated Angle θ (degrees):

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

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

The calculator uses the fundamental trigonometric ratios:

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

Where:

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

Details: These calculations are fundamental in construction, navigation, physics, and engineering applications.

Tips:

Q1: What's the Pythagorean theorem relationship?
A: \( hyp^2 = adj^2 + opp^2 \), which the calculator uses when two sides are known.

Q2: How precise are the calculations?
A: Results are accurate to 3 decimal places, sufficient for most practical applications.

Q3: Can I calculate area with this?
A: Not directly, but area = 0.5 × adj × opp once sides are known.

Q4: What if I know opposite and hypotenuse?
A: The calculator will determine adjacent using \( adj = \sqrt{hyp^2 - opp^2} \).

Q5: How are degrees converted for calculations?
A: Degrees are converted to radians internally using PHP's deg2rad() function.