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 TWOSIDES 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 = √a^{2 }– (b)^{2} In this triangle, a = 5 cm, b = 4 cm Hence, h = √5^{2} – (4)^{2} cm = √25 – 16 cm = 3 cm Now, A = ½ (b x h) = ½ (6 x 3) cm^{2} = 9 cm^{2}

Perimeter

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