Two sides of a triangle are 5 m and 8 m in length and the angle between them is increasing at a rate of 0.12 rad/s.

Question

Two sides of a triangle are 5 m and 8 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. 

Note: The area of A of a triangle given by the law of sines: A = (1/2)ab(sinθ), where a and b are two sides and θ is the angle between them.

Answer 1

A = 20sinθ

dA/dt = 20cosθ·dθ/dt = 1.2 m²/sec