Sides of a Triangle Formula
Before learning the sides of a triangle formula, let us recall a few things about a rightangled triangle. Sides of a rightangled triangle can be found out by using various methods like Pythagoras theorem or by using the perimeter of the triangle but sides of a triangle formula can be used to find the sides of the rightangled triangle quickly. For applying this method we just need to have one side of the triangle and an acute angle and we can find out the rest of the sides of the triangle. In the following section, we will learn about the sides of a triangle formula for the rightangled triangle.
What Are the Sides of A Triangle Formula?
The sides of a triangle formula of a given rightangled triangle is related to the trigonometric ratios. They are:
If we are given an angle and a side length,

Sine θ = Length of the opposite side / Length of the Hypotenuse side

Cos θ = Length of the adjacent side / Length of the Hypotenuse side

Tan θ = Length of the opposite side / Length of the adjacent side
et us see the applications of sides of a triangle formula in the following section.
Solved Examples Using Sides of A Triangle Formula

Example 1: What are the sides of the right triangular park whose hypotenuse is 10 in and having a base angle of 30°?
Solution:
To find: The side of a triangular park.
Given,
Hypotenuse = 10 in.
The base angle = 30 degrees
Using sides of a triangle Formula,
Sine θ = Length of opposite side / Length of Hypotenuse side
Sine 30° = x/10
x = 5 in
And, Cos θ = Length of adjacent side / Length of Hypotenuse side
Cos 30°= y/10
y = 5√3 in
Answer: The remaining sides of a triangular park are 5 in and 5√3 in.

Example 2: What are the sides of the right triangle whose adjacent side is 10√3 in and having a base angle of 60°?
Solution:
To find: The length of one side of a triangular park.
Given,
Adjacent side = 10√3 in.
The base angle = 60 degrees
Using sides of a triangle Formula,
Cos θ = Length of adjacent side / Length of Hypotenuse side
Cos 60°= 10√3/y
y = 20√3 in
And, Sine θ = Length of opposite side / Length of Hypotenuse side
Sine 60° = x/20√3
x = 30 in
Answer: The remaining sides of a triangular park are 30 in and 20√3 in.