The circle in the figure below has a radius of r and center at C. The distance from A to B is x, the distance from A to D is y, and the length of arc BD is s. Redraw the figure, label it asindicated, and solve the problem.If A31°, s = 12, and r = 14, find x. (Round your answer to the nearest whole number.)х 3ВхAу

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Asked Nov 21, 2019
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The circle in the figure below has a radius of r and center at C. The distance from A to B is x, the distance from A to D is y, and the length of arc BD is s. Redraw the figure, label it as
indicated, and solve the problem.
If A
31°, s = 12, and r = 14, find x. (Round your answer to the nearest whole number.)
х 3
В
х
A
у
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The circle in the figure below has a radius of r and center at C. The distance from A to B is x, the distance from A to D is y, and the length of arc BD is s. Redraw the figure, label it as indicated, and solve the problem. If A 31°, s = 12, and r = 14, find x. (Round your answer to the nearest whole number.) х 3 В х A у

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Expert Answer

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Step 1

 

First of all, redraw the figure and put the given values.

AB = x

BC = CD = 14

AD = 100

A = 31°

Arc BD = 12

14
в
A
31
12
14
100
D
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14 в A 31 12 14 100 D

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Step 2

Now using the arc length BD to find C.

ө
arc length 2Trx-
360
ө
2T x BCx-
3600
BD
BD 360°
ө
ВС
27T
12 360°
14
= 49.110°
ZC49° (rounding upto nearest whole number)
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ө arc length 2Trx- 360 ө 2T x BCx- 3600 BD BD 360° ө ВС 27T 12 360° 14 = 49.110° ZC49° (rounding upto nearest whole number)

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Step 3

Now find D using the sum of angles of a triangle law in ...

ZA+ZC+ZD = 180° (in aADC
31° 49° D = 180°
ZD 180° -31° - 49°
=1000
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ZA+ZC+ZD = 180° (in aADC 31° 49° D = 180° ZD 180° -31° - 49° =1000

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