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
The counter example: m∠ ABC = 35°, and m∠ CBD = 25°.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. When two planes intersect each other will create an angle.
Point C is the interior of ABD.
The measure of angle ABD is 60°.
The measure of angle ABC is 40°.
The measure of angle CBD is 20°.
Now when we add the angle ABC and CBD:
∠ ABC + ∠ CBD = 40° + 20°
∠ ABC + ∠ CBD = 60°
∠ ABC + ∠ CBD = ∠ ABD
The counter-example will be:
∠ ABD = ∠ ABC + ∠ CBD
60° = 35° + 25°
Therefore,
∠ ABC = 35° and ∠ CBD = 25°
Learn more about angle here:
brainly.com/question/22323626
#SPJ9
Answer:
21.71% increase
Step-by-step explanation:
increase = Increase ÷ Original Number × 100
12756/58753*100
0.217112318*100
21.71% increase.
MARK ME BRAINLIEST
meters cube or m³
Volume uses '³' or cube units on 3d models.
Area uses '²' or square units on 2d models.
32 is your initial value, because that is what he starts with
