Question

What is the area of her pasture if she decides to make two sides of 500 ft. Each and uses the angle you found in part (a)?

Answer 1

(a) The angle between them is 90 degrees

(b) The area is 125000ft^2

Explanation:

Given

See attachment for complete question

Solving (a): Angle that gives the maximum area.

The area of a triangle is:

`Area = (1)/(2)abSinC`

Where C is the angle between a and b.

The maximum area of a triangle is:

`Max\ Area = (1)/(2)ab`

Equate both areas to find C

`(1)/(2)ab\ sinC = (1)/(2)ab`

Divide both sides by
`(1)/(2)ab`

`sinC = 1`

Take arc sin of both sides

`C = sin^(-1)(1)`

`C = 90`

The angle between them is 90 degrees

Solving (b): The area when
`a = b =500`

The area of a triangle:

`Area = (1)/(2)abSinC`

So:

`Area = (1)/(2) * 500 * 500 * sin(90)`

`Area = (1)/(2) * 500 * 500 * 1`

`Area = (250000)/(2)`

`Area = 125000`