Question

A rain 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 = 60°, what is the area of the opening?
1.2 in2

7.9 in2

16.3 in2

20.8 in2

Answer 1

The statement gives you the function that models the Area as a function of angle theta, and is telling the value of this angle.

Then, you only need to replace the value of the angle in the function, to obtain the requested area.

A(Θ) = 16 sin Θ • (cos Θ + 1).

Θ = 60°

A(60°) = 16 sin(60°) * [cos(60°) + 1 ] = 16 * (√3) / 2 * [1/2 + 1] = 8(√3) * 3/2 = 12√3 ≈ 20.79

 Answer: 20.8 in^2