An Isosceles triangle has two equal sides of length 10cm. Let x be the angle between the two equal sides.
a. Express the area A of the triangle as a function of x in radians.
b. Suppose that x is increasing at the rate of 10 degrees per minute. How fast is A changing at the instant x = pi/3? At what value of x will the triangle have a maximum area?
The Attempt at a Solution
For part A, I know the answer is 50sin(x) using the double angle formula
For max area, using optimization techniques:
A'=50cosx >0 for 0<x<pi/2 and 3pi/2<x<2pi (since dimensions can't be negative)
A' <0 for pi/2<x<3pi/2
A'= 0 for x= pi/2 and 3pi/2
Using closed interval method:
A(3pi/2)=-50, therefore A will be max when x=pi/2
I put this in another thread from about a year ago but the information was scrambled and I didn't receive any feedback, anyone mind taking a look at this to see if it's correct?