A footbridge is in the shape of an arc of a circle. the bridge is 10 ft tall and 27 ft long, horizontally. what is the radius of the circle that contains the bridge? round your answer to the nearest tenth.

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10-05-2018
Mathematics

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A footbridge is in the shape of an arc of a circle. the bridge is 10 ft tall and 27 ft long, horizontally. what is the radius of the circle that contains the bridge? round your answer to the nearest tenth.

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calculista calculista · Answer 1 · 2018-05-19T20:38:15+02:00

calculista calculista

19-05-2018

see the picture attached to better understand the problem

we know that
the bridge is 10 ft tall and 27 ft long, horizontally
so
BC=10 ft
DE=27 ft---------> DC=27/2----> 13.5 ft
DA=r (radius of the circle)
AC=r-10

Applying the Pythagoras Theorem
DA²=DC²+AC² ------> r²=13.5²+(r-10)²----> r²=182.25+r²-20r+100
20r=282.25--------> r=14.11 ft

the answer is
r=14.11 ft

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