Math

Right Triangle Calculator

Find missing sides and angles.

Input Values

Adjust parameters below

Side A (Leg)

Side B (Leg)

RESULT

Hypotenuse (c)

NUMBER

Angle A

36.87°

Angle B

53.13°

Area

💡

Step-by-Step Solution

How this result was calculated

Given legs: a = 3, b = 4

Calculate Hypotenuse (c) using Pythagoras theorem: c = √(a² + b²)

c = √(9 + 16) = √25.00 = 5.0000

Calculate Angle A: A = arcsin(a/c)

A = arcsin(3/5.0000) = 36.87°

Calculate Angle B: B = 90° - A

B = 90° - 36.87° = 53.13°

Calculate Area: Area = 0.5 * a * b

Area = 0.5 * 3 * 4 = 6.00

How It Works

Guide and Formula

Right Triangle Calculator

This calculator finds all properties of a right triangle given the two legs (perpendicular sides).

Pythagorean Theorem:

a^2 + b^2 = c^2

Where:

a, b = The two legs (perpendicular sides)

c = The hypotenuse (longest side)

Trigonometric Relationships:

sin(A) = a/c (opposite/hypotenuse)

cos(A) = b/c (adjacent/hypotenuse)

tan(A) = a/b (opposite/adjacent)

What You Get

1. Hypotenuse (c): Calculated using √(a² + b²)

2. Angles A & B: Found using inverse trigonometric functions

3. Area: Computed as (1/2) × a × b

?FAQs

What is a right triangle?

A right triangle has one angle equal to 90°. The side opposite this angle is called the hypotenuse.

How do I find the hypotenuse?

Use the Pythagorean theorem: c = √(a² + b²), where a and b are the lengths of the two legs.

Can I use this if I know the hypotenuse?

This calculator requires the two legs as input. If you have the hypotenuse, you can find a leg using: a = √(c² - b²).

What are the 3-4-5 triangles?

These are special right triangles with sides in the ratio 3:4:5. They're commonly used in construction because they form perfect right angles.