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

Question

ELEN [110]

4 years ago

6

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.

Mathematics

1 answer:

lilavasa [31] · Answer 1 · 2022-01-22T06:30:15+03:00

See the picture attached to better understand the problem

we know that
<span>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
DA</span>²=DC²+AC²<span> ------> r</span>²=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