Question

from his home, justin would have to walk due north to get to his friend hassan’s house and due east to get to his friend ellen’s house. it is 4 miles from justin’s house to ellen’s house and a straight - line distance of 5 miles from hassan’s house to ellen’s house. how far is justin’s house from hassan’s house?
□ miles

Explanation:

Step1: Identify right triangle sides

Let Justin's home = $J$, Hassan's = $H$, Ellen's = $E$. $JH = x$ (unknown), $JE = 4$, $HE = 5$. $\triangle JHE$ is right-angled at $J$.

Step2: Apply Pythagorean theorem

$$JH^2 + JE^2 = HE^2$$
$$x^2 + 4^2 = 5^2$$

Step3: Solve for $x$

$$x^2 = 25 - 16 = 9$$
$$x = \sqrt{9} = 3$$

Answer:

3 miles