Calculus Question

Question

Two sides of a triangle are 4 m and 7 m in length and the angle between them is increasing at a rate of 0.12 rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3.

Answer 1

Areas = 0.5·4·7sinθ = 14sinθ m²; ds/dt = 14cosθdθ/dt = 14cosπ/3·0.12rad/s = 0.84 m²/s