Question

zoe is in a hot air balloon that has just taken off and is floating above its launching point. harry is standing on the ground, 6.5 meters away from the launching point. if zoe and harry are 9.6 meters apart, how high up is zoe? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Recognize right - triangle

The situation forms a right - triangle where the distance from Harry to the launching point is one leg ($a = 6.5$ meters), the distance between Zoe and Harry is the hypotenuse ($c=9.6$ meters), and the height of Zoe above the launching point is the other leg ($b$).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, so $b=\sqrt{c^{2}-a^{2}}$. Substitute $a = 6.5$ and $c = 9.6$ into the formula: $b=\sqrt{9.6^{2}-6.5^{2}}=\sqrt{(9.6 + 6.5)(9.6 - 6.5)}=\sqrt{16.1\times3.1}=\sqrt{49.91}\approx7.1$.

Answer:

$7.1$