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 of the opening may be expressed as the function: A(Θ) = 16 sin Θ • (cos Θ + 1). If Θ = 30°, what is the area of the opening?

Answer 1

A(30) = 16sin(30)[cos(30)+1]

(cos(30), sin(30)) = (sqrt(3)/2, 1/2)

A(30) = 16*(1/2) * [sqrt(3)/2 +1]

A(30) = 4*(sqrt(3)+2) = 14.93