Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is 𝜋 3 rad.

Question

Two sides of a triangle are 6 m and 9 m in length and the angle between them is increasing at a rate of 0.06 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 rad.

Answer 1

area A of triangle A = 1/2·6·9·sinθ = 27sinθ m²;

dA/dt = 27cosθdθ/dt = 27cosπ/3·0.06 m²/s = 0.81 m²/s