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Finding the length of a zip line (Measuring distance)

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A zip line runs from the top of a platform on the edge of a pond to the ground across the pond. A camp counselor places a mirror on the edge of the pond across from the platform and stands back until the top of the platform is visible in the mirror.

Find the length of the zip line. (Round your answer to the nearest foot.) ft

I started with this proportion solution but I know that this is only finding the height.

4/200=6/x

4x/4=1200/4

x=300

Now I am confused with the Pythagorean Theorem portion to find the length. Or am I just overly confusing and combining random formulas? HELP!!!

a^2 + b^2 = c^2

6^2 + 4^2= 52

c^2= 52 or 2√13

Jul 18, 2021
edited by Guest  Jul 18, 2021

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Find the length of the zip line. (Round your answer to the nearest ft.)

Hello Guest!

You calculated correctly. The height of the tower is 300 ft.

Now follows Pythagoras:

$$z^2=200^2ft^2+300^2ft^2\\ z=\sqrt{(200^2+300^2)ft^2}\\ z=\sqrt{(130\ 000)ft^2}\\ \color{blue}z=360.555ft$$

The length of the zip line is 361ft.

!

Jul 18, 2021