Question

Two sides of a triangle are $8$ m and $5$ m in length. The angle between them is increasing at the rate $0.08$ rad/sec. When the angle between the sides is $\frac{\pi}{3}$, the rate at which the area of the triangle is increasing is:

• A. $0.4 \text{ m}^2/\text{sec}$
• B. $0.8 \text{ m}^2/\text{sec}$
• C. $0.6 \text{ m}^2/\text{sec}$
• D. $0.04 \text{ m}^2/\text{sec}$
• E. $0.08 \text{ m}^2/\text{sec}$

Hint:

In related rates problems involving triangles, if the side lengths are fixed, the only variable affecting the area is the angle. This makes the derivative much simpler than using Heron's formula or base/height methods.

Answer 1

The Correct Option is B