Thread: Trig problem I'm stuck on

I have a triangle that has internal angles of 35, 80 and 65 degrees. The area of the triangle needs to be 4000sq metres. Say I need to fence this triangle. Will 285 metres of fencing material be enough? If this is not enough fencing material can I change the side lengths of the triangle such that the area is still 4000sq m and no more than 285m of material is used? I'm not able to change the angles in this triangle by more than +or- 25 degrees.
Even just a suggestion as to where to start tackling this problem would be greatly appreciated.

Hello Eleven Eleven

Originally Posted by Eleven Eleven

I have a triangle that has internal angles of 35, 80 and 65 degrees. The area of the triangle needs to be 4000sq metres. Say I need to fence this triangle. Will 285 metres of fencing material be enough? If this is not enough fencing material can I change the side lengths of the triangle such that the area is still 4000sq m and no more than 285m of material is used? I'm not able to change the angles in this triangle by more than +or- 25 degrees.
Even just a suggestion as to where to start tackling this problem would be greatly appreciated.

I don't think you can quite do this with 285 m - the mimimum length of fencing you need will be 288 m.

Here's the calculation.

Suppose the triangle is with .

The area of the triangle is , and using the Sine Rule . So

This gives and . The perimeter is then m.

The minimum perimeter for a given area will be when the triangle is equilateral, all angles then being . But this gives each side as m, with a perimeter of just over m.

Grandad

That's great. It's got me started so thank you!