NDA 1 2025 Maths, question 47

Topic: Trigonometry

Passage · Q46 to Q47

In a triangle $ABC$ , two sides $BC$ and $CA$ are in the ratio $2:1$ and their opposite corresponding angles are in the ratio $3:1$ .

Q47

Consider the following statements: I. The triangle is right-angled. II. One of the sides of the triangle is 3 times the other. III. The angles $A$ , $C$ and $B$ of the triangle are in AP. Which of the statements given above is/are correct?

(a) I only
(b) II and III only
(c) I and III onlyCorrect answer
(d) I, II and III

Solution.

Answer: (c) I and III only

The sine rule gives $A = 90^{\circ}$ , $B = 30^{\circ}$ and $C = 60^{\circ}$ .
Statement I is true. The side lengths are in the ratio $2:1:\sqrt{3}$ .
No pair has ratio $3:1$ , so II is false.
The ordered angles $A,C,B$ are $90^{\circ},60^{\circ},30^{\circ}$ , an arithmetic progression with common difference $- 30^{\circ}$ .
Thus III is true.