Question

question 7. elizabeth is in the hot air balloon that has risen straight up. matthew is standing on the ground, 12 meters away from the launch point. if elizabeth and matthew are 15 meters apart, how high is elizabeth in the hot air balloon?

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the balloon be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 15\) (the distance between Elizabeth and Matthew), \(a=12\) (the horizontal distance from the launch - point to Matthew), and \(b = h\) (the height of the balloon). So \(h^{2}+12^{2}=15^{2}\).

Step2: Solve for \(h\)

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Answer:

Elizabeth is \(9\) meters high in the hot - air balloon.