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:
I belive the answer is 20 songs.
Step-by-step explanation:
The equation you're looking for to solve this is
0.30x+5=0.20x+7
Then, you would solve for x in order to get 20.
You didnt provide the selections, but some answers would most likely be rotations, translations, and reflections.
Answer: 17 people
Step-by-step explanation:
You divide 8 3/4 and 1/2 and you get 17 1/2
And since the question asks how many people can he serve you use the whole number because its not fair if you give a full serving to a person and half a serving to another.
Answer:
12
Step-by-step explanation:
Using the 30-60-90 triangle formula side AB would be double of side CB.
