I walk six miles in a straight line in a direction north of east,and I end up four miles north and several miles east.How many degrees north of east have I walked?
A)19°
B)42°
C)60°
D)71°

Question

Quizplus · Accepted Answer

We can draw a right-angled triangle where the hypotenuse is the distance covered by the person, which is 6 miles, and the vertical side represents the distance covered northwards, which is 4 miles.
Using Pythagoras theorem, we can find the length of the horizontal side: 
Horizontal side = sqrt(6^2 - 4^2) = 2√5 miles
The angle between the hypotenuse and vertical side represents the direction north of east.
tan θ = (opposite/adjacent) = (4/2√5) = 2/√5
θ = tan⁻¹(2/√5) = 41.81°
Therefore, the person walked 41.81° north of east, which is closest to 42° as given in option B.

I Walk Six Miles in a Straight Line in a Direction