Question

a drawbridge will sometimes open up to let boats and other water traffic pass through. as it opens, the surface of the drawbridge raises above the level of the roadway, as modeled by the function:
$r = \sqrt{h^2 + d^2}$
if the length of the drawbridge, $r$, is 18 meters, and the point $p$ is 7 meters above the roadway, what is the distance $d$?
image of a right triangle with hypotenuse $r$, one leg $d$, and the other leg $h$ (with point $p$ at the top of leg $h$)
a. 16.6 meters
b. 31 meters
c. 20.9 meters
d. 12 meters

Explanation:

Step1: Substitute known values

We know \( r = 18 \) meters and \( h = 7 \) meters. Substitute these into the formula \( r=\sqrt{h^{2}+d^{2}} \), we get \( 18=\sqrt{7^{2}+d^{2}} \).

Step2: Square both sides

To eliminate the square root, square both sides of the equation: \( 18^{2}=(\sqrt{7^{2}+d^{2}})^{2} \), which simplifies to \( 324 = 49 + d^{2} \).

Step3: Solve for \( d^{2} \)

Subtract 49 from both sides: \( d^{2}=324 - 49=275 \).

Step4: Solve for \( d \)

Take the square root of both sides: \( d=\sqrt{275}\approx16.6 \) meters.

Answer:

A. 16.6 meters