An isosceles triangle has two equal sides of length of 10cm. let theta be the angle between the two equal sides.a. express the area A of the triangle as a function of theta in radians. b. Suppose...

An isosceles triangle has two equal sides of length of 10cm. let theta be the angle between the two equal sides.

a. express the area A of the triangle as a function of theta in radians.

b. Suppose that theta is increasing at the rate of 10 degrees per minute. How fast is Achanging at the instant theta=pi/3, at what value of theta will the triangle have a maximum area ?

Asked on by bdremm

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lfryerda | High School Teacher | (Level 2) Educator

Posted on

I am very sorry, but I accidentally put an extra 0 in the numerator!! The number should actually be `{25pi}/9` not `{250pi}/9`.

Since the angle is changing at a rate of `pi/18` radians per minute, we have as an intermediate step `50cos theta {d theta}/{dt}` which simplifies to `50cos theta (pi/18)={50pi}/18 cos theta={25pi}/9 cos theta` .

Upon substituting `theta=pi/3` , we get:

`{dA}/{dt}={25 pi}/9(1/2)={25pi}/18`

The remainder of the question is still correct.

The rate of change is `{25pi}/18` and the maximum area is at `theta=pi/2` .

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