Question

alexa is mountain climbing with kendrick and has just climbed a 7 - meter vertical rock face kendrick is standing 6.5 meters away from the bottom of the cliff, looking up at alexa. how far away are alexa and kendrick? if necessary, round to the nearest tenth. meters submit

Explanation:

Step1: Apply Pythagorean theorem

The situation forms a right - triangle, where one leg \(a = 7\) (height of the rock face) and the other leg \(b=6.5\) (distance from Kendrick to the bottom of the cliff). The distance \(d\) between Alexa and Kendrick is the hypotenuse. By the Pythagorean theorem \(d=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 7\) and \(b = 6.5\) into the formula: \(d=\sqrt{7^{2}+6.5^{2}}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(7^{2}=49\) and \(6.5^{2}=42.25\). Then \(a^{2}+b^{2}=49 + 42.25=91.25\).
So \(d=\sqrt{91.25}\).

Step3: Find the square - root

\(\sqrt{91.25}\approx9.6\) (rounded to the nearest tenth).

Answer:

\(9.6\)