# Thread: Optimisation problem: isoscles triangle inscribed in semi-circle

1. ## Optimisation problem: isoscles triangle inscribed in semi-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.

2. Hello banana_banana
Originally Posted by banana_banana
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.
Let the angle between the radii forming the two equal sides of the triangle be $\theta$. Then the area of the triangle is given by

$A = \tfrac12.10^2\sin\theta = 50\sin\theta$

$\Rightarrow \frac{dA}{d\theta} = 50\cos\theta = 0$ when $\theta = \tfrac{\pi}{2}$

Can you finish it now?

3. ## > Optimisation problem: isoscles triangle inscribed in semi-circle

Originally Posted by Grandad
Hello banana_bananaLet the angle between the radii forming the two equal sides of the triangle be $\theta$. Then the area of the triangle is given by

$A = \tfrac12.10^2\sin\theta = 50\sin\theta$

$\Rightarrow \frac{dA}{d\theta} = 50\cos\theta = 0$ when $\theta = \tfrac{\pi}{2}$

Can you finish it now?

How can i finish? I am quite confused about this ? Would you like to explain it better?

4. Originally Posted by banana_banana
How can i finish? I am quite confused about this ? Would you like to explain it better?
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?

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### issocelesstriangle inscribed in a semicircle

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