Multiple choice

The arch of a bridge is in the form of an arc of a circle. If the span of the bridge is 40 m and height in the middle is 8 m, then what is the radius of curvature of the bridge?

  1. 25 m

  2. 27 m

  3. 29 m

  4. 31 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let radius be R. The span is 40, so half-span is 20. Height is 8. Using the property of a chord and sagitta: R^2 = 20^2 + (R-8)^2. R^2 = 400 + R^2 - 16R + 64. 16R = 464. R = 29.

AI explanation

The span of 40 m and the height of 8 m form a right triangle with the radius as the hypotenuse. Using the geometric property of circles, the radius squared equals 20 squared plus the quantity radius minus 8 squared. Expanding this gives r squared equals 400 plus r squared minus 16r plus 64. Solving for r results in a radius of 29 m.

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