Line Center

Determine the vertical distance from the center of the line to the tip of the arc.?

A 30″ horizonatal line connects at its ends an arc with a radius of 40″. Determine the vertical distance from the center of the line to the tip of the arc. Answer should be 2.919
How do I solve?

Let h = required distance.
Then, remainder of distance to centre of circle = 40 – h.
Then notice right-angled triangle with legs (40 – h) and 15 (half of horizontal line),
and hypotenuse equal to radius (40).
Thus, (40 – h)^2 + 15^2 = 40^2.
Solving for h gives 2 answers.
The smaller one is h = 40 – 5√(55) ≈ 2.919.

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About the Author:

Loan Modification Help Center is a free gathering place for resources and information on the rapidly evolving field of loan modifications. The internet is over flowing with information on this subject with the problem being that there can be as much bad information and advice as good. For a homeowner struggling with mortgage payments and facing the possibility of foreclosure, the importance of getting straightforward information with no agenda or ulterior motive is of utmost importance. The resources we make available at Loan Modification Help Center are just what homeowners need as they seek to understand their options and get the information they need to make the critical decisions involved in a loan modification. For more information visit loanmodificationhelpcenter.org.

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