Question 1177018: Topic: Similarities (I don't know if proofs is the right section)
You are estimating the height of a semicircle arch...
https://media.discordapp.net/attachments/802751414874537995/821167758799798292/wOUqIvRsLZcfAAAAABJRU5ErkJggg.png
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
The height of the arch at the center is the radius of the semicircle.
Picture the 5 foot distance from the ground to the arch as a 5-foot pole.
Draw the radius of the semicircle to the top of the pole.
The diagram now shows a right triangle with one leg 5, hypotenuse equal to the radius of the circle, and the other leg 1 less than the radius of the circle (because the foot of the pole is 1 foot away from the end of the arch).
Use the Pythagorean Theorem to solve for the radius of the arch given the right triangle with legs 5 and r-1 and hypotenuse r.
A student with a lot of experience might recognize those lengths as the 5-12-13 Pythagorean Triple.
ANSWER (which could be obtained by solving the equation using the Pythagorean Theorem): The radius of the semicircle, and therefore the height of the arch at the center, is 13 feet.
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