Question

heather is playing hide - and - seek with larry and tony. larry is hiding 8.9 meters south of heather, and tony is hiding 3.9 meters east of larry. how far apart are heather and tony? if necessary, round to the nearest tenth.
□ meters
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Explanation:

Step1: Identify the right triangle

Heather, Larry, and Tony form a right triangle. The distance from Heather to Larry (8.9 m) is one leg, and the distance from Larry to Tony (3.9 m) is the other leg. We need to find the hypotenuse (distance between Heather and Tony) using the Pythagorean theorem: \(c = \sqrt{a^2 + b^2}\), where \(a = 8.9\), \(b = 3.9\), and \(c\) is the distance between Heather and Tony.

Step2: Calculate \(a^2\) and \(b^2\)

First, calculate \(a^2\): \(8.9^2 = 79.21\)
Then, calculate \(b^2\): \(3.9^2 = 15.21\)

Step3: Sum the squares

Add the two results: \(79.21 + 15.21 = 94.42\)

Step4: Take the square root

Find the square root of 94.42: \(\sqrt{94.42} \approx 9.7\)

Answer:

9.7