Right Triangle Trigonometry Formulas

Right Triangle Formulas:

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

Angle (θ):

degrees

Opposite Side:

meters

Adjacent Side:

meters

Hypotenuse:

meters

Calculated Angle (θ):

Calculated Opposite Side:

Calculated Adjacent Side:

Calculated Hypotenuse:

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1. What is Right Triangle Trigonometry?

Definition: The study of relationships between angles and sides in right-angled triangles.

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

2. Key Trigonometric Formulas

The three primary trigonometric functions for a right triangle:

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

Where:

\( \theta \) — One of the non-right angles in the triangle (degrees)
\( opp \) — Length of side opposite to angle θ (meters)
\( adj \) — Length of side adjacent to angle θ (meters)
\( hyp \) — Length of the hypotenuse (meters)

3. Pythagorean Theorem

For any right triangle:

\[ hyp^2 = opp^2 + adj^2 \]

4. Using the Calculator

Tips: Enter any two values (angle + one side, or two sides) and the calculator will compute the remaining values.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: The calculator uses meters for lengths and degrees for angles, but any consistent units will work.

Q2: How precise are the calculations?
A: Results are accurate to 3 decimal places for lengths and 2 decimal places for angles.

Q3: What if I know two sides but no angle?
A: The calculator will use the Pythagorean theorem and inverse trig functions to find the angle.

Q4: Can I use this for non-right triangles?
A: No, these formulas are specific to right triangles. For other triangles, use the Law of Sines or Cosines.

Q5: Why does angle θ need to be between 0-90 degrees?
A: In a right triangle, the non-right angles must be acute (less than 90°).