# Right Triangle

## Definition

Right triangle is a figure where one of the three angles measures 90° and the other two angles are acute that sums to 90°.

## Properties

1. One of the three angles is always 90°, and the sum of the other two angles equals 90°;

in ∆ABC, ∠ABC = 90° and ∠BAC + ∠ACB = 90°

2. The angle formed between the base and altitude is always the right angle. In ∆ABC, AB = altitude and BC = base, so ∠ABC = right angle

3. The hypotenuse is the longest side of a right angle-triangle, so AC is the longest side

## Types

Right triangles are classified into two types: 1) right scalene triangle, and 2) right isosceles triangles.

The differences between the types are given below:

## Formulas

### Area

Area (A) = ½ (b × h), where b = base and h = height

Problem: Finding the area of a right triangle when only TWO SIDES are known

Find the area of a right triangle whose hypotenuse is 5 cm and base is 4 cm

Solution:

Here we will use the Pythagoras theorem to calculate the height of the triangle,
(hypotenuse)2  =  (height)2 + (base)2
Let, a = hypotenuse,
b = base,
h = height
The equation becomes,
h = √a2 – (b)2
In this triangle, a = 5 cm, b = 4 cm
Hence, h = √52 – (4)2 cm
= √25 – 16 cm
= 3 cm
Now, A = ½ (b x h)
= ½ (6 x 3) cm2
= 9 cm2

### Perimeter

Perimeter (P) = a + b + c, where a, b, c are the measures of three sides