Optimisation problem: isoscles triangle inscribed in semi-circle

banana_banana · #1 $Old$ July 4th, 2009, 09:13 AM

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.

Grandad · #2 $Old$ July 4th, 2009, 09:22 AM

Hello banana_banana

Quote:

Originally Posted by banana_banana $View Post$

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

banana_banana · #3 $Old$ July 5th, 2009, 12:10 AM

Quote:

Originally Posted by Grandad $View Post$

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?

mr fantastic · #4 $Old$ July 5th, 2009, 12:22 AM

Quote:

Originally Posted by banana_banana $View Post$

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?