|
Question 545406: An arch for a bridge over a highway is in the form of a semiellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height is 31 feet from the center is to be 16 feet above the ground.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! An arch for a bridge over a highway is in the form of a semiellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height is 31 feet from the center is to be 16 feet above the ground.
**
Standard form of equation for an ellipse with vertical major axis:
(x-h)^2/b^2+(y-k)^2/a^2=1,a>b, (h,k)=(x,y) coordinates of center.
..
For given problem:
Place center of ellipse, (0,0) at center of bridge at ground level.
Given length of vertical major axis=70=2a
a=35
a^2=1225
..
Equation of ellipse:
x^2/b^2+y^2=1
plug in coordinates of given point on ellipse(31, 16)
31^2/b^2+16^2/a^2=1
961/b^2+256/1225=1
961/b^2=1-256/1225=.791
b^2=961/.791≈1215
b≈34.86
length of minor axis=2b≈69.71 ft
span of bridge≈69.71 ft
|
|
|
| |
