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
An input is were you put a number to get the answer. a output is were you take away the answer to get the correct
Answer:
SAS
Step-by-step explanation:
The two triangles share a side, so that would be reflexive to show that side is congruent. Also, keep in mind that all right angles are congruent! The picture already tells us that the two outer side are congruent. So in conclusion, the two angles are congruent by SAS.
Hope this helps! :)
Um... it'll take each pipe 80 mins, bcz if together they take that long, then to find the pipes time separately, you just multiply it by two to show it doing the work the other pipe did as well. Is that what you wanted??
Put the answer choice numbers where the x’s are in the equation and then solve. The ones that are equal to 0 once solved will be your answer
