Question

a utility pole is 6 miles high. a 7 miles cable is stretched from the top of the pole to a stake in the ground how far is the stake from the pole?
□ miles
round your answer to the nearest hundredth.
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Explanation:

Step1: Identify the problem type

This is a right triangle problem where the utility pole is one leg (\(a = 6\) miles), the cable is the hypotenuse (\(c = 7\) miles), and the distance from the stake to the pole is the other leg (\(b\)). We use the Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\).

Step2: Rearrange the formula to solve for \(b\)

We get \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(a = 6\) and \(c = 7\) into the formula: \(b=\sqrt{7^{2}-6^{2}}=\sqrt{49 - 36}=\sqrt{13}\).

Step3: Calculate the numerical value

\(\sqrt{13}\approx3.61\) (rounded to the nearest hundredth).

Answer:

\(3.61\)