NIMCET Properties Of Triangle Previous Year Questions (PYQs) – Page 3 of 3
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Showing 24 questions
The perimeter of a $\Delta ABC$ is 6 times the arithmetic mean of the sines of its angles. If the side a is 1, then the angle A is
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Solution
Quick Solution
Given: Perimeter = 6 × Arithmetic Mean of sin A, sin B, sin C
Using Law of Sines: \( \frac{a}{\sin A} = 2R \), and a = 1 ⇒ \( \sin A = \frac{1}{2R} \)
Assume \( A = 30^\circ \Rightarrow \sin A = \frac{1}{2} \Rightarrow 2R = 2 \)
⇒ b = 2 sin B, c = 2 sin C
Perimeter = \( 1 + b + c = 1 + 2 \sin B + 2 \sin C \)
Mean = \( \frac{\sin A + \sin B + \sin C}{3} \)
Check: \( 1 + 2\sin B + 2\sin C = 6 \cdot \frac{1/2 + \sin B + \sin C}{3} \) ✅
✅ Final Answer: 30°
In ΔABC, if a = 2, b = 4 and ∠C = 60°, then A and B are respectively equal to
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Solution
If the angles of a triangle are in the ratio 2 : 3 : 7, then the ratio of the sides opposite to these
angles is
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Solution
A harbour lies in a direction 60° South of West from a fort and at a distance 30 km from it, a ship sets out from the harbour at noon and sails due East at 10 km an hour. The time at which the ship will be 70 km from the fort is
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Solution
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