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 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

The area using the formula is 14.928 sq in.

Answer 2

Answer: Area of opening is 14.928 sq. inches.

Explanation:

Since we have given that

Area of the opening is expressed as

`A(\theta)=16\sin \theta* (\cos \theta +1)`

We have given that θ = 30°,

so, our area becomes,

`A(30^\circ)=16\sin 30^\circ* (\cos 30^\circ+1)\\\\A(30^\circ)=16* (1)/(2)((√(3))/(2)+1)\\\\A(30^\circ)=(8)/(2)(√(3)+2)\\\\A(30^\circ)=4* 3.7320\\\\A(30^\circ)=14.928`

Hence, Area of opening is 14.928 sq. inches.