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:
a < - 3
Step-by-step explanation:
Given
- 2a > 6
Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity, thus
a < - 3
Well, we dont know because we cant see the barmodels
11/7
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Answer:Kyle’s claim is not reasonable
Step-by-step explanation:
Total length of the string of the necklace that Kyle covered with black beads is 5/8.
Total length of the string of the necklace that Kyle covered with white beads is 1/4.
Total length of the string of the necklace that Kyle covered with black beads and white beads is would be
1/4 + 5/8 = 7/8 = 0.875
Kyle thought that he will cover 6/12 of the string with beads. 6/12 = 0.5
It means that he covered more than 6/12. Kyle's claim was wrong
