SOLUTION: The right end point of an arc is tangent to a horizontal line. The arc length is 12. The left end point of the arc is 4 units above the horizontal line. How do you find the arc rad

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Question 950327: The right end point of an arc is tangent to a horizontal line. The arc length is 12. The left end point of the arc is 4 units above the horizontal line. How do you find the arc radius?
Thank you for solving this and showing me how.
Found 2 solutions by Alan3354, Fombitz:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The right end point of an arc is tangent to a horizontal line. The arc length is 12. The left end point of the arc is 4 units above the horizontal line. How do you find the arc radius?
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It appears that this is not possible.
I know how to solve it, but the distance to the tangent point cannot be 12 units.
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I mistakenly labeled the horizontal distance as 12 also.
It's always hard to locate your own mistakes.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

From the arc length,
R%2Atheta=12
The blue line is the bisector of angle theta.
You know that,
Y=Rsin%28theta%2F2%29
The angle in the small triangle opposite the length 4 is also theta%2F2.
So then,
sin%28theta%2F2%29=4%2F%282Y%29=2%2FY
Substituting,
sin%28theta%2F2%29=2%2F%28Rsin%28theta%2F2%29%29
sin%28theta%2F2%29%5E2=2%2FR
From the arc length,
theta=12%2FR
theta%2F2=6%2FR
Substituting,
%28sin%286%2FR%29%29%5E2=2%2FR
Iterating using EXCEL,
R=17.3
theta=39.74degrees