SOLUTION: The arch of a bridge is an arc of a circle. The distance between the ends of the arc is 56 cm and the clearance of the arch above the water is 9.8 m. Find the radius of the arc.
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Question 982633: The arch of a bridge is an arc of a circle. The distance between the ends of the arc is 56 cm and the clearance of the arch above the water is 9.8 m. Find the radius of the arc.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The arch of a bridge is an arc of a circle.
The distance between the ends of the arc is 56 METERS and the clearance of the arch above the water is 9.8 m.
Find the radius of the arc.
:
draw this out. The chord of the circle will be 56 m long.
let x = dist from center and middle of the chord, (the water)
then the radius will be (x+9.8)
:
Note; two right triangles formed by half the chord (28m), x,
and the radius (hypotenuse)
:
Using pythag; a^2 + b^2 = c^2, we can write this problem like this
= r
replace r with (x+9.8)
= x + 9.8
Square both sides
x^2 + 28^2 = (x+9.8)^2
FOIl the right side
x^2 + 784 = x^2 + 19.6x + 96
Subtract x^2 and 96 from both sides
784 - 96 = 19.6x
19.6x = 688
x = 688/19.6
x = 35.1
Find the radius
r = 35.1 + 9.8
r = 44.9 meters is the radius
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