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

`√(x^2+y^2)=2.17`

and

`\tan29.6^\circ=\frac yx`

Solve the system to get

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

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