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?

Answer 1

A(45degrees) = 16sin(45)(cos(45)+ 1)
= 16(1/sqrt2)(1+1/sqrt2)
= 16(1/sqrt2)(1+ sqrt2) /sqrt2
= 16(1+sqrt2) /2
= 8 + (sqrt2)/2in^2