Question

jareds work
a 16 - meter zipline is being installed. the first zipline platform is 10 meters above the ground, and the second platform is 4 meters above the ground. how far apart are the platforms?
jareds work to set up the problem is shown.
is he correct? if not, explain his mistake.
line 1: ( a = 10+4 = 14 )
line 2: ( 14^{2}+b^{2}=16^{2} )
jared is incorrect. in line 1, he should have subtracted 4 from 10 instead of adding them.
jared is incorrect. in his sketch, 16 and b should be switched.

Explanation:

Step1: Apply Pythagorean theorem

The horizontal distance between platforms is \(a\), vertical difference is \(10 - 4 = 6\) meters, zip line length is 16 meters. So \(a^2 + 6^2 = 16^2\).

Step2: Calculate correct values

\(a^2 + 36 = 256\) → \(a^2 = 256 - 36 = 220\) → \(a = \sqrt{220} \approx 14.83\). Jared used vertical difference as 4 instead of 6, so his setup is wrong.

Answer:

Jared is incorrect. In his setup, he used the vertical height of the second platform (4m) instead of the vertical difference between the two platforms (10m - 4m = 6m). The correct vertical side in the Pythagorean theorem should be 6m, not 4m.