Finding the Height of a Triangle Using Related Rates

[franz32]

Hello here's the problem:

Each of the two sides of a triangle are increasing at the rate of 1/2 foot per second, and the included angle is decreasing 2 degrees per second. Find the rate of change of the area when the sides and included angle are respectively 5ft., 8ft., and 60 deg.

Here is my question: How do I find the height of the triangle?
Say my base is 5ft. How do I express it in terms of the given details in the problem?

 

[matt grime]

Try finding a better formula for the area of a triangle involving the two given sides and the included angle. (Think vector cross products, perhaps.)

 

[HallsofIvy]

Area= (1/2) height times base where the "height" is measured perpendicular to the "base". Take one of the given sides as base, and drop a perpendicular to it. The other given side is the hypotenuse of the right triangle formed. The height you need is the "opposite side" of that right triangle.