Question

matt is in a hot air balloon that has just taken off and is floating above its launching point. janet is standing on the ground, 6.3 meters away from the launching point. if matt and janet are 9.9 meters apart, how high up is matt? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Apply Pythagorean theorem

Let the height of Matt be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 6.3\), \(c=9.9\), and \(b = h\). So \(h=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(a = 6.3\) and \(c = 9.9\) into the formula: \(h=\sqrt{9.9^{2}-6.3^{2}}=\sqrt{(9.9 + 6.3)(9.9 - 6.3)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).
First, calculate \(9.9+6.3 = 16.2\) and \(9.9 - 6.3=3.6\). Then \(h=\sqrt{16.2\times3.6}=\sqrt{58.32}\).

Step3: Calculate the square - root

\(\sqrt{58.32}\approx7.6\)

Answer:

\(7.6\)