Two sides of a triangle are 10 m and 12 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 the rate of

We have two sides of a triangle are 10 m and 12 m in length and the angle between them is increasing at a rate of 0.06 rad/s.

Area of the triangle =

Differentiating it w.r.t

At ,

Therefore the area of the triangle is increasing at the rate of

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1.8 m²/s

Step-by-step explanation:

A = ½(10)(12)sin(theta)

A = 60sin(theta)

dA/d(theta) = 60cos(theta)

At theta = pi/3,

dA/d(theta) = 60cos(pi/3) = 30

dA/dt = dA/d(theta) × d(theta)/dt

dA/dt = 30 × 0.06

dA/dt = 1.8 m²/d

pi x^2

step-by-step explanation:

pi times x squared