Optimisation problem: isoscles triangle inscribed in semi-circle

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July 4th 2009, 07:13 AM
banana_banana

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.
July 4th 2009, 07:22 AM
Grandad

Hello banana_banana

Quote:

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?

Grandad
July 4th 2009, 10:10 PM
banana_banana

> Optimisation problem: isoscles triangle inscribed in semi-circle

Quote:

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?

Grandad

How can i finish? I am quite confused about this ? Would you like to explain it better?
July 4th 2009, 10:22 PM
mr fantastic

Quote:

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?