Right Triangle Calculator

Enter Base (b):

Enter Height (h):

A right triangle is a triangle in which one of the angles is exactly 90 degrees. These triangles are one of the most important shapes in geometry, frequently used in trigonometry, architecture, and engineering. Understanding how to calculate the sides, angles, and area of a right triangle can be very useful in a wide range of practical applications.

Key Components of a Right Triangle

Hypotenuse: The longest side of the triangle, opposite the right angle.
Legs: The two shorter sides that form the right angle.
Angles: The right angle (90°) and the two other angles that add up to 90°.

Calculating the Hypotenuse

To calculate the hypotenuse (c) when the two legs (a and b) are known, you can use Pythagoras' Theorem:

$c = \sqrt{a^2 + b^2}$

Where:

a = Length of one leg
b = Length of the other leg
c = Hypotenuse

Calculating the Legs

If you know the hypotenuse (c) and one leg (a or b), you can calculate the missing leg using the rearranged Pythagorean theorem:

$a = \sqrt{c^2 - b^2} \quad \text{or} \quad b = \sqrt{c^2 - a^2}$

Calculating Angles

The two non-right angles can be calculated using trigonometric functions like sine, cosine, and tangent.

To find angle A (opposite side a):
$\sin(A) = \frac{a}{c} \quad \Rightarrow \quad A = \sin^{-1}\left(\frac{a}{c}\right)$
To find angle B (opposite side b):
$\sin(B) = \frac{b}{c} \quad \Rightarrow \quad B = \sin^{-1}\left(\frac{b}{c}\right)$

Calculating the Area

The area of a right triangle is calculated using the following formula:

$\text{Area} = \frac{1}{2} \times a \times b$

Where:

a = Length of one leg
b = Length of the other leg

Example Calculations

If the legs of the right triangle are 3 and 4:
$c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$
The hypotenuse is 5.
To calculate the area:
$\text{Area} = \frac{1}{2} \times 3 \times 4 = 6$

Why Use a Right Triangle Calculator?

Geometry and Trigonometry: Right triangles are fundamental in trigonometry, where angles and sides are crucial in solving problems.
Real-World Applications: Architects, engineers, and construction workers use right triangles in designing buildings, bridges, and other structures.
Quick Solutions: A calculator allows for fast, accurate calculations without manually solving each equation.

Benefits of Using a Right Triangle Calculator

A right triangle calculator simplifies the process of finding unknown sides, angles, and areas. By inputting the known values, the calculator instantly provides the results, helping with both basic geometry problems and advanced trigonometric applications. It saves time, ensures accuracy, and is a great tool for students and professionals alike.