Thread: On applications of partial derivatives

Two sides of a triangle were measured as 150 and 200 feet, and the included angle is 60 degrees. If the possible errors are 0.2 feet in measuring the sides and 1 degree in the angle, what is the greatest possible error in the computed area?
(Use the total differential)
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I have an idea on how to do it, but it's a very long process. Does anyone have a simpler solution?

The Area of the triangle is one half the Area of the parallelogram

formed by 2 vectors

A = 1/2|UxV| = 1/2 |U||V|sin(t)

Write this as A =1/2 xy sin(t) x= 150 y = 200 and t = pi/3

dA = 1/2 [(ysin(t) dx + xsin(t)dy + xycos(y)dt]

for dt make sure to use use pi/180