Right Triangle Calculator

Right Triangle Formulas:

\[ c = \sqrt{a^2 + b^2} \] \[ \text{Area} = \frac{1}{2} \times a \times b \] \[ \theta = \arctan\left(\frac{b}{a}\right) \]

Hypotenuse (c):

Area:

Angle θ (opposite side b):

Definition: This calculator computes the hypotenuse, area, and angles of a right triangle based on the lengths of its two legs.

Purpose: It helps students, engineers, and designers quickly solve right triangle problems in geometry, construction, and technical applications.

The calculator uses these fundamental right triangle formulas:

\[ c = \sqrt{a^2 + b^2} \] \[ \text{Area} = \frac{1}{2} \times a \times b \] \[ \theta = \arctan\left(\frac{b}{a}\right) \]

Where:

Explanation: The Pythagorean theorem calculates the hypotenuse, while trigonometric functions determine the angles.

Details: Right triangle geometry is fundamental in construction, navigation, engineering, and physics for solving distance and angle problems.

Tips: Enter any two known values (a and b). All values must be positive numbers. The calculator will compute all other properties.

Q1: What if I only know one side and the hypotenuse?
A: Rearrange the Pythagorean theorem: \( b = \sqrt{c^2 - a^2} \), then use the calculator.

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

Q3: Can I use different units?
A: Yes, as long as you use consistent units for both sides (all in meters, feet, etc.).

Q4: What's the angle opposite side a?
A: It's \( 90° - \theta \) since angles in a triangle sum to 180°.

Q5: How is the area formula derived?
A: A right triangle is half of a rectangle with sides a and b, hence \( \frac{1}{2}ab \).