Question

three ballet dancers are positioned on stage. jane is straight behind ernest and directly left of mariana. if ernest and jane are 8.8 feet apart, and mariana and ernest are 9.4 feet apart, what is the distance between jane and mariana? if necessary, round to the nearest tenth.

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Explanation:

Step1: Identify the triangle type

The positions form a right triangle, with Ernest - Jane as one leg (\(a = 8.8\) ft), Ernest - Mariana as the hypotenuse (\(c = 9.4\) ft), and Jane - Mariana as the other leg (\(b\)).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Rearranging for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).
Substitute \(a = 8.8\) and \(c = 9.4\):
\(b=\sqrt{9.4^{2}-8.8^{2}}=\sqrt{(9.4 + 8.8)(9.4 - 8.8)}=\sqrt{18.2\times0.6}=\sqrt{10.92}\approx3.3\)

Answer:

\(3.3\)