Question

A person desires to reach a point that is 2.17 km from her present location and in a direction that is 29.6° north of east. However, she must travel along streets that are oriented either north-south or east-west. What is the minimum distance she could travel to reach her destination?

Answer 1

She needs to move $x$ km in the east-west direction and $y$ km in the north-south direction so that

$\sqrt{x^2+y^2}=2.17$

and

$\tan29.6^\circ=\dfrac yx$

Solve the system to get

$x=1.89\,\mathrm{km}$

$y=1.07\,\mathrm{km}$