Answer:
(a) The angle between them is 90 degrees
(b) The area is 125000ft^2
Step-by-step explanation:
Given
See attachment for complete question
Solving (a): Angle that gives the maximum area.
The area of a triangle is:
[tex]Area = \frac{1}{2}abSinC[/tex]
Where C is the angle between a and b.
The maximum area of a triangle is:
[tex]Max\ Area = \frac{1}{2}ab[/tex]
Equate both areas to find C
[tex]\frac{1}{2}ab\ sinC = \frac{1}{2}ab[/tex]
Divide both sides by [tex]\frac{1}{2}ab[/tex]
[tex]sinC = 1[/tex]
Take arc sin of both sides
[tex]C = sin^{-1}(1)[/tex]
[tex]C = 90[/tex]
The angle between them is 90 degrees
Solving (b): The area when [tex]a = b =500[/tex]
The area of a triangle:
[tex]Area = \frac{1}{2}abSinC[/tex]
So:
[tex]Area = \frac{1}{2} * 500 * 500 * sin(90)[/tex]
[tex]Area = \frac{1}{2} * 500 * 500 * 1[/tex]
[tex]Area = \frac{250000}{2}[/tex]
[tex]Area = 125000[/tex]
