Answer:1.1 ft^2
Step-by-step explanation:
Φ=55°
Radius=r=4
π=3.14
Area of segment=area of sector - area of triangle
Area of sector=Φ/360 x π x r x r
area of sector=55/360 x 3.14 x 4 x 4
Area of sector=(55x3.14x4x4) ➗ 360
Area of sector=2763.2 ➗ 360
Area of sector=7.7 ft^2
Area of triangle=0.5 x r x r x sinΦ
Area of triangle=0.5 x 4 x 4 x sin55
Area of triangle=0.5 x 4 x 4 x 0.8192
Area of triangle=6.6 ft^2
Area of segment=area of sector - area of triangle
Area of segment=7.7-6.6
Area of segment=1.1 ft^2
The diagram can be redrawn as,
The value of x and y can be determined as,
![\begin{gathered} \tan C=\frac{AB}{BC} \\ \tan 45^{\circ}=\frac{x}{7\sqrt[]{2}} \\ x=7\sqrt[]{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctan%20C%3D%5Cfrac%7BAB%7D%7BBC%7D%20%5C%5C%20%5Ctan%2045%5E%7B%5Ccirc%7D%3D%5Cfrac%7Bx%7D%7B7%5Csqrt%5B%5D%7B2%7D%7D%20%5C%5C%20x%3D7%5Csqrt%5B%5D%7B2%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} \cos C=\frac{BC}{AC} \\ \cos 45^{\circ}=\frac{7\sqrt[]{2}}{y} \\ y=14 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ccos%20C%3D%5Cfrac%7BBC%7D%7BAC%7D%20%5C%5C%20%5Ccos%2045%5E%7B%5Ccirc%7D%3D%5Cfrac%7B7%5Csqrt%5B%5D%7B2%7D%7D%7By%7D%20%5C%5C%20y%3D14%20%5Cend%7Bgathered%7D)
Thus, option (D) is the correct solution.
Plot point F where angle alpha is located.
Triangle ABF has two interior angles x and 80. They add to the exterior angle alpha due to the remote interior angle theorem.
alpha = x+80
<h3>
Answer: Choice D</h3>
Answer:
(9,3)
Step-by-step explanation:
