IPMAT Indore 2025 · Quantitative Ability · Question 22
IPMAT Indore 2025 previous year question on Trigonometry, with the answer and a step-by-step solution.
- A\sin \theta
- B\cos \theta
- C2\cos \theta
- D2\sin \theta
Answer & solution
Answer: Option D
Step 1 — recall the extended Law of Sines. In any triangle with circumradius R,
\frac{\text{side}}{\sin \left( \text{angle opposite that side}\right)}=2R
Step 2 — pick the right side-and-angle pair. We know the angle \theta at vertex B. The side opposite B is AC, and we are told AC=x. The circumradius is y, so R=y:
\frac{AC}{\sin B}=2R \Rightarrow \frac{x}{\sin \theta}=2y
Step 3 — rearrange.
\frac{x}{y}=2\sin \theta
Note the isosceles condition AB=AC (which forces \angle ACB=\theta as well) is not actually needed — it is there to make the figure consistent.
Answer: Option 4 — 2\sin \theta
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