Henry walks 20 km west forgot his coat, so he turns and heads 13 km east. He decided to go another path to make up for the lost time and travels 30 km south and then moves west for 27 km. Calculate Henry's displacement.

D = -20 + 13 - 30i - 27 = -34 - 30i

tan Ar = -30/-34 = 0.88235
Ar = 41.42o = Reference angle.
A = 41.42 + 180 = 221.4o

D = -34/cos221.4 = 45.3km[221.4o].

To calculate Henry's displacement, we need to determine the net distance and direction from his starting point to his ending point.

First, let's establish the coordinate system. We'll consider west and south as negative directions, and east and north as positive directions.

Henry walks 20 km west. This means he moves 20 km in the negative x-direction (west).

Then, Henry realizes he forgot his coat and turns around, heading 13 km east. This means he travels 13 km in the positive x-direction (east). At this point, he has covered a net distance of 20 km - 13 km = 7 km west.

Next, Henry decides to take a detour. He travels 30 km south. This means he moves 30 km in the negative y-direction (south).

Finally, Henry moves west for 27 km. This means he moves 27 km in the negative x-direction (west).

Now, let's add up the distances and determine the net displacement.

Net displacement in the x-direction = -7 km (7 km west minus 0 km east)
Net displacement in the y-direction = -30 km (0 km north minus 30 km south)

To calculate Henry's displacement, we can use the Pythagorean theorem in a right-angled triangle formed by the x and y components of displacement.

Displacement = sqrt((Net displacement in the x-direction)^2 + (Net displacement in the y-direction)^2)
= sqrt((-7 km)^2 + (-30 km)^2)
= sqrt(49 km^2 + 900 km^2)
= sqrt(949 km^2)
≈ 30.8 km

Therefore, Henry's displacement is approximately 30.8 km.