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)
-------
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
  |
LinkBack URL
About LinkBacks