What is the ratio of the area of sector ABC to the area of sector DBE?
2 answers:
The area of sector ABC is = x. The area of sector DBE is = y. The ratio of the area ABC to the area of DBE = x/y (x over y OR x divided by y)
We have to find the" ratio of the area of sector ABC to the area of sector DBE".
Now,
the general formula for the area of sector is
Area of sector= 1/2 r²θ
where r is the radius and θ is the central angle in radian.
180°= π rad
1° = π/180 rad
For sector ABC, area= 1/2 (2r)²(β°)
= 1/2 *4r²*(π/180 β)
= 2r²(π/180 β)
For sector DBE, area= 1/2 (r)²(3β°)
= 1/2 *r²*3(π/180 β)
= 3/2 r²(π/180 β)
Now ratio,
Area of sector ABC/Area of sector DBE =
= 4/3
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For this you would use the "angle bisector theorem," which states that the ratio of the other two sides are proportional to the two segments of the divided base (opposite the bisected angle). See attached image...
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