Question

to get from home to his friend russells house, omar would have to walk 1 mile due north. to get from home to his friend hectors house, omar would have to walk 4 miles due east. what is the straight - line distance between russells house and hectors house? if necessary, round to the nearest tenth. miles

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem. The path from home to Russell's (1 mile north) and home to Hector's (4 miles east) form the two legs of a right - triangle. Let \(a = 1\) and \(b = 4\).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 1\) and \(b = 4\) into the formula: \(c=\sqrt{1^{2}+4^{2}}=\sqrt{1 + 16}=\sqrt{17}\).

Step3: Calculate the value

\(\sqrt{17}\approx4.1\) (rounded to the nearest tenth).

Answer:

\(4.1\)