Question

the end of a dogs leash is attached to the top of a 5 - foot - tall fence post, as shown in the diagram below. the dog is 7 feet away from the base of the fence post. how long is the leash, to the nearest tenth of a foot? 9.0 8.6 12.0 4.9

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 5\) (height of the fence post), \(b=7\) (distance from the base of the post to the dog), and \(c\) is the length of the leash.
Substitute the values: \(5^{2}+7^{2}=c^{2}\).
Calculate \(5^{2}=25\) and \(7^{2} = 49\). Then \(25 + 49=c^{2}\), so \(c^{2}=74\).

Step2: Solve for \(c\)

Take the square root of \(74\), \(c=\sqrt{74}\).
Using a calculator, \(\sqrt{74}\approx8.6\)

Answer:

B. \(8.6\)