Question

three ballet dancers are positioned on stage. if sidney is 6 meters straight behind lucia and 5 meters directly left of tiana, how far is lucia from tiana? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Identify right - triangle

The positions of Sidney, Lucia, and Tiana form a right - triangle. The two legs of the right - triangle have lengths \(a = 6\) meters and \(b = 5\) meters. We want to find the length of the hypotenuse \(c\) (the distance between Lucia and Tiana).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 6\) and \(b = 5\) into the formula: \(c=\sqrt{6^{2}+5^{2}}=\sqrt{36 + 25}=\sqrt{61}\).

Step3: Calculate and round

\(\sqrt{61}\approx 7.8\) (rounded to the nearest tenth).

Answer:

7.8