Question

Suppose you walk 19.5 m straight west and then 27.0 m straight north. How far are you, in meters, from your starting point? What is the compass direction, in degrees measured West of North, of a line connecting your starting point to your final position

Answer 1

To find the distance from the starting point, use the Pythagorean theorem. The compass direction can be found using the tangent function. The distance from the starting point is approximately 33.32 m and the compass direction is approximately 55.94° west of north.

Step-by-step explanation:

To find the distance from the starting point, we can use the Pythagorean theorem. The 19.5 m distance west and the 27.0 m distance north form a right triangle. Using the theorem, the distance from the starting point is:

√((19.5^2) + (27.0^2)) = √((380.25) + (729)) = √(1109.25) = 33.32 m

To find the compass direction, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 27.0 m (north) and the adjacent side is 19.5 m (west). The tangent of the angle is:

tan(θ) = 27.0 / 19.5
θ = atan(27.0 /19.5) = 55.94°

Therefore, the distance from the starting point is approximately 33.32 m and the compass direction is approximately 55.94° west of north.