CUET · MATHS · PYQ PAPER 2023
The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is \(\theta=60^{\circ}\), is :
- A \(30 cm^2 /\) radian
- B \(120 cm^2 /\) radian
- C \(30 \sqrt{3} cm^2 / radian\)
- D \(60 \sqrt{3} cm^2 /\) radian
Answer & Solution
Correct Answer
(A) \(30 cm^2 /\) radian
Step-by-step Solution
Detailed explanation
A = \(\frac{1}{2} ab \sin\theta\) \(\frac{dA}{d\theta} = \frac{1}{2} ab \cos\theta\) \(\frac{dA}{d\theta} = \frac{1}{2} (10)(12) \cos(60^{\circ})\) \(\frac{dA}{d\theta} = 60 \cdot \frac{1}{2} = 30 cm^2 / radian\)
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