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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 A of the opening may be expressed as the function: A(θ) = 16 sin θ ⋅ (cos θ + 1). If θ = 45°, what is the area of the opening?

User Major Byte
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1 Answer

5 votes

Answer:


4(2+√(2))\text{ square unit}

Explanation:

Given function that shows the area of the opening,


A(\theta)=16 \sin\theta (\sin \theta + 1)

If
\theta = 45^(\circ)

Hence, the area of the opening would be,


A(45^(\circ))=16 \sin 45^(\circ) (\cos 45^(\circ) + 1)


=16* (1)/(√(2))* ((1)/(√(2))+1)


=16((1)/(2)+(1)/(√(2)))


=8+(16)/(√(2))


=8+4√(2)


=4(2+√(2))\text{ square unit}

User Weeniearms
by
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