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

Answer:

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

Step-by-step 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

$\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1$

now, we can plug

a=200

b=100

$\frac{x^2}{200^2}+ \frac{y^2}{100^2}=1$

we can plug x=50 and find y

$\frac{50^2}{200^2}+ \frac{y^2}{100^2}=1$

$y=25\sqrt{15}$

$y=97ft$