Question

19 multiple choice 1 point paige is in a hot air balloon that has just taken off and is floating above its launching point. ryan is standing on the ground, 12 meters away from the launching point. if paige and ryan are 15 meters apart, how high up is paige? 7 meters 15 meters 12 meters 9 meters

Explanation:

Step1: Identify right - triangle sides

We have a right - triangle where the distance from Ryan to the launching point is one leg ($a = 12$ meters), the distance between Paige and Ryan is the hypotenuse ($c=15$ meters), and the height of Paige above the launching point is the other leg ($b$).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, so $b^{2}=c^{2}-a^{2}$. Substitute $a = 12$ and $c = 15$: $b^{2}=15^{2}-12^{2}=225 - 144=81$.

Step3: Solve for $b$

Take the square root of both sides: $b=\sqrt{81}=9$ meters.

Answer:

D. 9 meters