Question

A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet. What is the height of the tunnel 5 feet from the edge? Round your answer to the hundredths place.

9.99 feet
13.82 feet
24.65 feet
25.01 feet

Answer 1

The height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

What is an ellipse?

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

A tunnel is constructed with a semi-elliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet.

2a = 60 (width of the tunnel is 60 feet)

a = 30

And the maximum height at the center of the tunnel is 25 feet

b = 25

Let's assume the center of the ellipse is at the origin.

So the equation of the ellipse:

$\rm \dfrac{x^2}{30^2}+\dfrac{y^2}{25^2}=1$

Now plug x = a - 5 = 30 - 5 = 25

$\rm \dfrac{25^2}{30^2}+\dfrac{y^2}{25^2}=1$

After solving:

$\rm \dfrac{y^2}{25^2}=1-\dfrac{25}{36}$

$\rm y^2=\dfrac{6875}{36}$

y = ±13.819 ≈ ±13.82

Height cannot be negative

y = 13.82 feet

Thus, the height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

Learn more about the ellipse here:

https://brainly.com/question/19507943

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