Two sides of a triangle are 8 m and 10 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.

The area of the triangle is increasing at a rate 1.2 m²/s.

Step-by-step explanation:

Given sides of a triangle are 8 m and 10 m in length.

The angle between the sides of the triangle is increasing at a rate 0.06 rad/s.

It means

If the sides of a triangle are a and b and θ is the angle of the sides.

The area of the triangle is A =

Here, a = 8 m and b = 10 m

Differentiating with respect to t

putting the value of

                =1.2 m²/s

The area of the triangle is increasing at a rate 1.2 m²/s.