The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Answer:
93
Step-by-step explanation:
in your answer, give the measure of Angle C and explain how you calculated it.
i dont know the answer but i just added 3(29+2) and got 29 sorry if its wrong
Answer:
each bottle of juice costs $2.34
Step-by-step explanation:
2.74+10x=26.14
10x=26.14-2.74
10x=23.40
x=23.40/10
x=2.34
Answer:
8:07 am
Step-by-step explanation:
It takes 9 minutes to walk from his house to the bus station. It then takes 92 minutes for the bus to travel from Birmingham to Coventry. After arriving, he takes 12 minutes to reach his workplace. This takes a total of 113 minutes.
9 + 92 + 12 = 113
Convert 113 minutes to hours and minutes.
113 - 60 = 53
1 hr and 53 min
He has to be at work by 10. Subtract the time it takes to get to his work by the time he has to get there.
10 - 1 hr = 9
9 - 53 min = 8:07
The latest time he can leave is 8:07.
