So I got the answer wrong, and I really can not figure this out can someone show

Question

So I got the answer wrong, and I really can not figure this out can someone show me how to do this? I attached the image below, I got 68 km as my answer. I dont know what I am doing wrong.

A hiker makes four straight-line walks

A 28 km at 220? angle

B 14 km at 349? angle

C 20 km at 58? angle

D 15 km at 164? angle

in random directions and lengths starting at

position (41 km, 41 km)

How far from the starting point is the hiker

after these four legs of the hike? All angles

are measured in a counter-clockwise direction

from the positive x-axis.

Answer in units of km

So I got the answer wrong, and I really can not figure this out can someone show me how to do this? I attached the image below, I got 68 km as my answer. I dont know what I am doing wrong. A hiker makes four straight-line walks A 28 km at 220? angle B 14 km at 349? angle C 20 km at 58? angle D 15 km at 164? angle in random directions and lengths starting at position (41 km, 41 km) How far from the starting point is the hiker after these four legs of the hike? All angles are measured in a counter-clockwise direction from the positive x-axis. Answer in units of km

Explanation / Answer

r = 28cos220i + 28sin220 j + 14cos349 i + 14sin349 j + 20cos58 i +20sin58j + 15cos164i + 15sin164j

= - 11.53 i + 0.426 j

magnitude= sqrt(11.53^2 + 0.426^2) =11.54 km

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