The lengths of two sides of a triangle are 7 cm and 8 cm respectively and the measure of the angle included between these two sides is 60°. The length (in cm) of the third side of the triangle is :

Correct option is D

Given:

Two sides of a triangle: 7 cm and 8 cm

Included angle: 60°

Formula Used:

Cosine Rule (Law of Cosines):

​$$c^2 = a^2 + b^2 - 2ab\cos(C)$$​​

where a, b, c are the sides

Solution: 

a = 7, b = 8, C = 60^∘

Using cosine rule;

​$$c^2 = 7^2 + 8^2 - 2 \times 7 \times 8 \times \cos(60^\circ) \\ \ \\ c^2 = 49 + 64 - 112 \times 0.5 = 113 - 56 = 57 \\ \ \\ c = \sqrt{57} \,\text{cm}$$​​