The two sides of a tringle are increasing at the rate of 1/2 ft/sec with their included angle decreasing at the rate of π/90 rad/sec. What is the rate of change of area when the sides and the included angle are respectively 5 ft,8 ft, and 60°?

The two sides of a tringle are increasing at the rate of 1/2 ft/sec with their included angle decreasing at the rate of π/90 rad/sec. What is the rate of change of area when the sides and the included angle are respectively 5 ft,8 ft, and 60°?
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1 Answer

Answer :

Area = (L1 L2) sin(angle) , where L1, L2 and and angle are functions of time t. Take the derivative using the multiplication rule. The derivative will equal (L1L2)(derivative of sin) + sin times the derivative of L1 L2. You will have to use the multiplication rule a second time to get the derivative of L1 L2. Good luck.
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