Question

from his home, keenan would have to walk due north to get to his friend ashleys house and due east to get to his friend ryans house. it is 4.1 miles from keenans house to ryans house and a straight - line distance of 5.9 miles from ashleys house to ryans house. how far is keenans house from ashleys house? if necessary, round to the nearest tenth. miles submit

Explanation:

Step1: Identify the right - triangle

Let \(a\) be the distance from Keenan's house to Ashley's house, \(b = 4.1\) miles (Keenan to Ryan), and \(c=5.9\) miles (Ashley to Ryan). By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), so \(a^{2}=c^{2}-b^{2}\).

Step2: Substitute the values

Substitute \(b = 4.1\) and \(c = 5.9\) into the formula \(a^{2}=c^{2}-b^{2}\).

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Step3: Solve for \(a\)

Take the square root of both sides: \(a=\sqrt{18}\approx4.2\)

Answer:

\(4.2\)