Posted by **Isabel** on Wednesday, February 20, 2013 at 10:21pm.

A bridge is the shape of an arc of a circle. The bridge is 8 feet tall and 36 feet wide. What is the radius of the circle that contains the bridge? Round your answer to the nearest tenth.

- Geometry (immediate help and explanation) -
**Reiny**, Wednesday, February 20, 2013 at 10:44pm
Assuming that the 36 feet wide line base is NOT a diameter, make a sketch

let the radius be x

then I see a right-angled triangle where

(x-8)^2 + 18^2 = x^2

x^2 - 16x + 64 + 324 = x^2

-16x = -388

x = 24.25

- Geometry (immediate help and explanation) -
**Isabel**, Wednesday, February 20, 2013 at 10:51pm
Thanks! But one question..um, where did you get the triangle?

- Geometry (immediate help and explanation) -
**Reiny**, Wednesday, February 20, 2013 at 10:56pm
draw a whole circle

draw a chord AB, your base , = 36

From the centre O draw a line OA , a radius

let the radius be x

so OA = x, the hypotenuse

from the centre draw a perpendicular to AB to hit AB at C

from C to the circle is 8 , so OC = x-8

OCA is a right - angled triangle.

so ...

see above

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