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°?

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.

Correction – you don’t have to use the multiplication rule twice. You just have area = (½t)(½t)sin(angle). One difficulty I see is that we don’t know the initial values of side lengths or the angle, so I don’t see how they can be related to one another. For example, the sides should be (s1 + ½t) and (s2+½t) for initial lengths s1 and s2

You may be able to use the specified lengths and angle as the initial ones and set time to 0