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alisha [4.7K]
3 years ago
12

A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, thi

s 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?
Mathematics
2 answers:
weqwewe [10]3 years ago
4 0
We are already given with the function to solve for the area:
<span>A(θ) = 16 sin θ ⋅ (cos θ + 1)
</span>
We simply have to substitute the value of the angle into the function. So,
If <span>θ = 90°,
A(</span>90°) = 16 sin (90°) ( cos (<span>90°) + 1 )

Using the calculator or the definition of trigonometric functions at angle of </span><span>90°, we get the value of the area:
</span>A(<span>90°) = 16 square inches</span>
hoa [83]3 years ago
4 0

we know that

The area A of the opening may be expressed as the function:

A(\alpha) = 16 sin \alpha* (cos  \alpha + 1)

For \alpha =90°

We simply have to substitute the value of the angle into the function

so

A(90) = 16*sin 90* (cos 90 + 1)

A(90) = 16*(1)* (0 + 1)

A(90) = 16  in^{2}

therefore

the answer is

the area of the opening is 16  in^{2}

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