4. Find the area of the largest isosceles triangle inscribed in a semi-circle of radius 10 ft, the vertex of the triangle being at the center of the circle.
4. Find the area of the largest isosceles triangle inscribed in a semi-circle of radius 10 ft, the vertex of the triangle being at the center of the circle.
Hello banana_bananaLet the angle between the radii forming the two equal sides of the triangle be $\displaystyle \theta$. Then the area of the triangle is given by
$\displaystyle A = \tfrac12.10^2\sin\theta = 50\sin\theta$
$\displaystyle \Rightarrow \frac{dA}{d\theta} = 50\cos\theta = 0$ when $\displaystyle \theta = \tfrac{\pi}{2}$
Can you finish it now?
Grandad
Grandad's reply does not require 'better' explaining. What needs better explaining is your reply. Specifically, what is it that you didn't understand in Grandad's reply. eg. Are you familiar with the area formula that has been used? If not, then how are we meant to know this unless you say so.
By the way, did you bother to draw a diagram of the problem?