Two sides of a triangle are 7 m 7 m and 12 m 12 m in length and the angle between them is increasing at a rate of 0.06 rad/s 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 π3 rad.

1.26 m^2 / s.

Step-by-step explanation:

The area A of the triangle = 1/2*7*12 sin x = 42 sin x where x is the angle between the lines.

Relation between the rates is

dA/dt + dA/dx * dx/dt

We are given that dx / dt = 0.06 rad/s.

A = 42 sin x

dA/dx = 42 cos x

So dA/dt = 42 cos x * 0.06

When x = π/3 (I am assuming that π 3 means π divided by 3):

dA/dt = 42 cos π/3 * 0.06

= 1.26 m^2/s.