In the triangle below, what is the length of the side opposite the 60° angle?

Solution:

Given,

In triangle ABC, ∠ C = 30°,∠ A = 60°, and ∠ B = 90°. y = 3.

A 30-60-90 triangle is a special triangle since the length of its sides is always in a consistent relationship with one another.

The side that is opposite to the 30° angle, AB = y will always be the smallest since 30° is the smallest angle in this triangle.

The side that is opposite to the 60° angle, BC = y × √3 = y√3 will be the medium length because 60° is the mid-sized degree angle in this triangle.

On the side that is opposite to the 90° angle, the hypotenuse AC = 2y will be the largest side because 90° is the largest angle.

In a 30-60-90 triangle, the ratio of the sides is always in the ratio of 1:√3: 2. This is also known as the 30-60-90 triangle formula for sides. y:y√3:2y.

BC = y√3.

BC = 3√3.

BC = 5.196

Therefore, BC = 5.196

In the triangle below, what is the length of the side opposite the 60° angle?

Summary:

The length of the side opposite the 60° angle is  5.196