A bird flies 2.0km south and then 1.5km 37∘ east of south. How far will it have to fly to get back to its original place if it flies in a straight line?

Question

I tried to draw a drawing of this to illustrate it, but all I have is an obtuse triangle with a side of 2, a side of 1.5 and an angle of 37 (but when added with 90 becomes the obtuse angle). I guessed earlier and found out the answer was 3.3 since it was a multiple choice answer, but how do I get 3.3? I know that I'd use the law of vector addition but how am I supposed to apply it?? I can't just add 2 and 1.5 to get 3.3.

Answer 1

use the law of cosines. The distance z is
z^2 = 2^2 + 1.5^2 - 2*2*1.5 cos127°
z = 3.14 km

Answer 2

wait. But the correct answer is 3.3 so now I'm even more confused

Answer 3

also we never learned about the law of cosines in physics? I don't know anymore physics is messing me up

Answer 4

To do the vector addition, just add the x- and y-components together to get the resultant.

Then get the length in the usual way.

Surely your text has examples of vector addition, and how to obtain the components of a vector.