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

Question

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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Reagan 1 week 2021-11-25T17:23:34+00:00 1 Answer 0 views 0

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    2021-11-25T17:24:45+00:00

    Answer:

    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

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