Question

A man drove 13 miles directly east from his home, made a left turn at an intersection, and then traveled 5 miles due north to his place of work. If a road was made directly from his home to his place of work, what would its distance be?

Answer 1

$\text{Let the man drove 13 miles  directly east from home, A and reach an}\\ \text{intersection point B. Then take a left turn and traveled 5 miles due north}\\ \text{to reach his place of work C.}\\ \\ \text{now if a road was made directly from his home to his place of work,}\\ \text{the distance AC can be found using the Pythagorean theorem. so we have}$

$(AC)^2=(AB)^2+(BC)^2\\ \\ \Rightarrow (AC)^2=(13)^2+(5)^2\\ \\ \Rightarrow (AC)^2=169+25\\ \\ \Rightarrow (AC)^2=194\\ \\ \Rightarrow AC=\sqrt{194}\\ \\ \Rightarrow AC \approx 13.93$

Hence the distance from his home to work place is approximately 13.93 miles