A deer runs 88 feet to the east, then turns and runs at an angle of 11 ° north of west for 127 feet. What is the direction of the deer's resultant vector?

Question

Asked before but I meant to put direction not magnitude, thank you!

Answer 1

We can place this scenario into a coordinate plane with the deer's original position at the origin and the positive x-axis pointing east. Then, the first leg of the deer's journey moves him to the point (88, 0) and the second leg moves him 127 × sin 101° in the positive y-direction (north) and 127 × cos 101° in the positive x-direction (east). Since cos 101° is negative, the deer actually moves west in that second leg, decreasing its x-coordinate. The angle of 101° is 11° more than a right angle, because the problem states that the deer runs at an angle 11° west of north in its second leg.

To answer the question, we find the ratio of the y-coordinate and x-coordinate of the deer at the end of its second leg, and then take the inverse tangent (because tan θ = y/x if θ is the angle between the positive x-axis and the line through the origin and the point (x, y).) So, this angle is tan^-1 ((127 × sin 101°)/(88 + 127 cos 101°)) = 62.91° to two decimal places. So the direction of the deer's resultant vector is 62.91° north of east.