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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?

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The area using the formula is 14.928 sq in.

Answer: Area of opening is 14.928 sq. inches.

Step-by-step explanation:

Since we have given that

Area of the opening is expressed as

[tex]A(\theta)=16\sin \theta\times (\cos \theta +1)[/tex]

We have given that θ = 30°,

so, our area becomes,

[tex]A(30^\circ)=16\sin 30^\circ\times (\cos 30^\circ+1)\\\\A(30^\circ)=16\times \frac{1}{2}(\frac{\sqrt{3}}{2}+1)\\\\A(30^\circ)=\dfrac{8}{2}(\sqrt{3}+2)\\\\A(30^\circ)=4\times 3.7320\\\\A(30^\circ)=14.928[/tex]

Hence, Area of opening is 14.928 sq. inches.

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