NDA 1 2025 Maths, question 37

Topic: Trigonometry

Passage · Q36 to Q38

The sides of a triangle $ABC$ are $AB = 3$ cm, $BC = 5$ cm and $CA = 7$ cm.

Q37

What is $\angle B$ equal to?

(a) $60^{\circ}$
(b) $105^{\circ}$
(c) $120^{\circ}$ Correct answer
(d) $150^{\circ}$

Solution.

Answer: (c) $120^{\circ}$

At $B$ , the adjacent sides are $AB = 3$ and $BC = 5$ , and the opposite side is $AC = 7$ .
By the cosine rule, $\cos B = \frac{3^{2} + 5^{2} - 7^{2}}{2 \cdot 3 \cdot 5} = - \frac{1}{2}$ .
As $0^{\circ} < B < 180^{\circ}$ , this gives $B = 120^{\circ}$ .