Question

A bridge over a gorge is supported by an arch in the shape of a semi-ellipse. The length of the bridge is 400 ft. and the maximum height is 100 ft. Draw a picture of the problem and label it with numeric values. Find the height of the arch 50 ft. from the center. Round to the nearest foot.

Answer 1

The height of the arch 50ft from the center is 97ft

Explanation:

A bridge over a gorge is supported by an arch in the shape of a semi-ellipse

The length of the bridge is 400 ft. and the maximum height is 100 ft

so, a=200ft

b=100ft

(a)

we can draw picture

(b)

now, we can use equation of ellipse formula

`(x^2)/(a^2)+ (y^2)/(b^2)=1`

now, we can plug

a=200

b=100

`(x^2)/(200^2)+ (y^2)/(100^2)=1`

we can plug x=50 and find y

`(50^2)/(200^2)+ (y^2)/(100^2)=1`

`y=25√(15)`

`y=97ft`