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A triangle has two constant sides of length 3 feet and 5 feet. the angle between these two sides is increasing at a rate of 0.1 radians per second. find the rate at which the area of the triangle is changing when the angle between the two sides is π/6.

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sqdancefan

Answer:

  dA/dt = 0.375√3 ft² ≈ 0.6495 ft²/s

Step-by-step explanation:

The area is given by the formula ...

  A = (1/2)ab¡sin(C)

where a and b are side lengths, and C is the angle between them. Differentiating, we have ...

  dA/dt = (1/2)ab¡cos(C)¡dC/dt

Filling in the given information, we get ...

  dA/dt = (1/2)(3 ft)(5 ft)(cos(π/6))(0.1 rad/s) = 0.75(√3)/2 ft²/s

  dA/dt = 0.375√3 ft² ≈ 0.6495 ft²/s

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