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# ) Find the length of the zip line.

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300
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Help me Find the length of the zip line.

I thought it was 210 .....

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.

140 ft

(a) Are the two triangles formed similar? Explain your reasoning.

Both triangles are right triangles. The angles made at the mirror on the ground are congruent. Therefore, the triangles  are  similar.

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

Sep 9, 2018

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The smaller triangle has a hypotenuse length of $$\sqrt{4^2+6^2} = \sqrt{52}=2\sqrt{13}$$

as the triangles are similar the zip line will have the same ratio to that hypotenuse as the 140 ft leg does to the 4 ft leg.

$$\dfrac{140}{4} = 35 \cdot 2\sqrt{13} = 70\sqrt{13}$$

and thus the zip line has length $$70\sqrt{13} \approx 252 ft$$

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Sep 9, 2018
edited by Rom  Sep 9, 2018