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
[tex]\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1[/tex]
now, we can plug
a=200
b=100
[tex]\frac{x^2}{200^2}+ \frac{y^2}{100^2}=1[/tex]
we can plug x=50 and find y
[tex]\frac{50^2}{200^2}+ \frac{y^2}{100^2}=1[/tex]
[tex]y=25\sqrt{15}[/tex]
[tex]y=97ft[/tex]
