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 = 90°, what is the area of the opening? A. 21.8 in^2 B. 16.0 in^2 C. 7.9 in^2 D. 1.0 in^2

Answer 1

Just plug in the 30° into that equation.

A(30°) = 16sin(30°)(cos(30°) + 1)
   = 16(1/2)(1 + √3/2)
   = Approx 14.9 in²

So A is the answer.

Answer 2

The answer is letter B. 16.0 in^2

You may use this equation to solve for the area:
A(90∘)=16sin90∘(cos90∘+1)
=16×1×(0+1)
=16 in^2

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