Will fan and medal
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 = 30°, what is the area of the opening?

14.9in^2
16.0in^2
19.3in^2
20.8in^2

Question

Will fan and medal
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 = 30°, what is the area of the opening? 

14.9in^2
16.0in^2
19.3in^2
20.8in^2

anonymous · Answer

@jim_thompson5910 can you help? Or do you know anyone who can help?

jim_thompson5910 · Answer

$$\Large A(\theta) = 16*\sin(\theta)*(\cos(\theta) + 1)$$

$$\Large A(30^{\circ}) = 16*\sin(30^{\circ})*(\cos(30^{\circ}) + 1)$$

$$\Large A(30^{\circ}) = 16*\frac{1}{2}*(\frac{\sqrt{3}}{2} + 1)$$

$$\Large A(30^{\circ}) \approx 16*0.5*(0.866025 + 1)$$

$$\Large A(30^{\circ}) \approx ???$$

jim_thompson5910 · Answer

In step 3, I used the unit circle http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/1024px-Unit_circle_angles_color.svg.png

anonymous · Answer

So the answer would be A?

jim_thompson5910 · Answer

yeah I'm getting 14.9282 which rounds to 14.9

anonymous · Answer

That's what I got :) Thank you so much