Question

I walk five miles in a straight line in a direction north of east, and i end up three miles east and several miles north. How many degrees north of east have i walked?.

Answer 1

53 degrees

Step-by-step explanation:

Based on the information, we can draw a triangle with 5 as the hypotenuse, 3 as the adjacent side, and N as the opposite side.

After this, we need to use a trig function that relates the hypotenuse, adjacent side, and angle. The function used for this is cos.

We can use X as our unknown angle.

Cos(X)=(A/H) with X as the angle we are solving for, A as the length of the adjacent side, 3, and H as the length of the hypotenuse, 5.

To solve for X, the unknown angle, we need to move the cos to the other side, cos^-1 or arccos.

Thus:

X = Cos-1 (3/5) = 53.13 to two significant figures.

Thus, X=53 degrees walked.