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.

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Zaria English

Mathematics

5 September, 21:11

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.

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Emery Owen · Answer 1

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