Answer:
16 feet height of the arch at a distance of 30 feet from the center
Step-by-step explanation:
Given data
span = 100 feet
height = 20 feet
to find out
the height of the arch at a distance of 30 feet from the center
solution
we know the equation of elliptical i.e.
x²/a² + y²/b² = 1 ......................1
from question we can say that length of major axis i.e
2a = 100
so a = 50
and height is
b = 20
so put a and b in equation 1
x²/a² + y²/b² = 1
x²/50² + y²/20² = 1
x²/2500 + y²/400 = 1
y²/400 = 1 - x²/2500
y / 20 = [tex]\sqrt{1 - x^{2} /2500}[/tex]
y = 20 [tex]\sqrt{1 - x^{2} /2500}[/tex]
so now take value 30 for function f(30)
f(30) = 20 [tex]\sqrt{1 - x^{2} /2500}[/tex]
f(30) = 20 [tex]\sqrt{1 -30^{2} /2500}[/tex]
f(30) = 16 feet
so 16 feet height of the arch at a distance of 30 feet from the center
