Arain gutter is to be constructed of aluminum sheets 12 inches wide. after marking off a length of 4 inches from each edge, this length is bent up at an angle θ. the area a of the opening may be expressed as the function: a(θ) = 16 sin θ ⋅ (cos θ + 1). if θ = 90°, what is the area of the opening?

We are already given with the function to solve for the area:
A(θ) = 16 sin θ ⋅ (cos θ + 1)

We simply have to substitute the value of the angle into the function. So,
If θ = 90°,
A(90°) = 16 sin (90°) ( cos (90°) + 1 )

Using the calculator or the definition of trigonometric functions at angle of 90°, we get the value of the area:
A(90°) = 16 square inches