Question

tammy likes to skate at a game store that is due south of her school and due west of her favorite skate park. if the game store is 4 kilometers from her school and the straight - line distance between the school and the skate park is 9.3 kilometers, how far is the game store from the skate park? if necessary, round to the nearest tenth. kilometers submit

Explanation:

Step1: Recognize the right - triangle

The school, game store, and skate park form a right - triangle. Let the distance from the school to the game store be \(a = 4\) km, the distance from the school to the skate park be \(c=9.3\) km, and the distance from the game store to the skate park be \(b\). By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 4\) and \(c = 9.3\) into the formula \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=(9.3)^{2}-4^{2}\).
Calculate \((9.3)^{2}=9.3\times9.3 = 86.49\) and \(4^{2}=16\).
So \(b^{2}=86.49 - 16=70.49\).

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{70.49}\approx8.4\) (rounded to the nearest tenth).

Answer:

\(8.4\)