Can anyone help me with the following question? Thanks! The length x of a side o

Question

Can anyone help me with the following question? Thanks!

The length x of a side of a triangle is increasing at a rate of 3 in/s, the length y of another side is decreasing at a rate of 2 in/ s and the contained angle between these two sides, theta, is increasing at a rate of 0.05 rad/s. How fast is the area of the triangle changing when x =40 inches, y =50 inches and theta = [note: you need Heron's Formula, which says: Area = 1/2 ab sin(C) if you have a triangle with 2 known sides, a and b and theta is the included angle created by these two sides.]

Explanation / Answer

area, A = (1/2)*a*b*sin(C)

dA/dt = (1/2) a*b*cos(C) *dC/dt+ (1/2)*sin(C) * (a*db/dt + b* da/dt)

= (1/2)* ( 40*50*cos(pi/6)*0.05 + sin(pi/6) * ( 40*(-2) + 50*3) )

= 60.80 inch^2/ s

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