I walk six miles in a straight line in a direction north of east,and I end up two miles east and several miles north.How many degrees north of east have I walked?
A)19 $\degree$
B)45 $\degree$
C)60 $\degree$
D)71 $\degree$

Question

Quizplus · Accepted Answer

To find the angle north of east, we need to draw a right triangle with the hypotenuse representing the distance walked (6 miles), the adjacent side representing the distance walked east (2 miles), and the opposite side representing the distance walked north (unknown). We can use the trigonometric function tangent to find the angle opposite the north side.

tan θ = opposite/adjacent 
tan θ = (distance walked north) / 2 
θ = arctan ((distance walked north) / 2)

From the problem, we know that the distance walked north is several miles (let's call it x). So, we have:

θ = arctan (x/2)

Using the Pythagorean theorem, we can solve for x:

6^2 = 2^2 + x^2 
x = √32

So,

θ = arctan (√32 / 2)

Using a calculator, we find that θ ≈ 71.57 degrees. Rounding to the nearest degree, we get 72 degrees, which is closest to answer choice D, 71°F.

I Walk Six Miles in a Straight Line in a Direction