Question

(10.02 lc) 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?

Answer 1

From this statement "the area of the opening may be expressed as the function: a(θ) = 16 sin θ ⋅ (cos θ + 1).


if θ = 30°

We can substitute 30° in the expression a(θ) = 16 sin θ ⋅ (cos θ + 1) to get the area of the opening.


The area of the opening = 16 sin 30 ⋅ (cos 30 + 1)

                                        = 16x0.5 (0.866 + 1)

                                        = 8(1.866)

                                        = 14.93 sq. inch.

Answer 2

Answer:

The area of the opening = 19.04 inches²

Step-by-step explanation:

The expression for the area of the opening is given to be :

A(θ) = 16 sin θ ⋅ (cos θ + 1)

Now, θ is having value = 30°

So, to find the required area of the opening we simply put the given value of θ = 30° , and simplify the expression :

A(30) = 16×sin 30° ·(cos 30° + 1)

$\implies \text{Area = }16\times\frac{1}{\sqrt{2}}\cdot (\frac{1}{\sqrt{2}}+1)\\\\\implies Area=16\times 0.7\cdot (0.7 +1)\\\\\implies Area=11.2\times 1.7\\\\\bf\implies \textbf{Area = }19.04\thinspace{ inches^2}$