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 = 60°, what is the area of the opening?

1.2 in2

7.9 in2

16.3 in2

20.8 in2

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 A of the opening may be expressed as the function: A(Θ) = 16 sin Θ • (cos Θ + 1). If Θ = 60°, what is the area of the opening?

 1.2 in2

 7.9 in2

 16.3 in2

 20.8 in2

anonymous · Answer

$$16 \sin (\theta ) (\cos (\theta )+1)\text{/.}\, \theta \to 60 {}^{\circ} $$20.7846 or 20.8 rounded to the nearest 1/10.

anonymous · Answer

$$16 \sin (60 {}^{\circ}) (\cos (60 {}^{\circ})+1)=\frac{16}{2} \sqrt{3} \left(\frac{1}{2}+1\right)=12 \sqrt{3}=20.7846  $$

anonymous · Answer

Thank you for the medal.