In straight-line distance, how far is city C from city A?

Question

An airplane flies 200 km due west from city A to city B and then 300 km in the direction of 32.5° north of west from city B to city C.

(a) In straight-line distance, how far is city C from city A?
( km)

(b) Relative to city A, in what direction is city C?
(° north of west)

Answer 1

No, it is not an accute triangle.
Please read my answer to a previous and very simialar question--you can easily replace the data and get your answer.

The question:
An airplane flies 200 km due west from city A to city B and then 290 km in the direction of 27.5° north of west from city B to city C.
a) In straight-line distance, how far is city C from city A?
b) Relative to city A, in what direction is city C?

My answer:
Best Answer - Chosen By Voters
Such problem can be solved systematically with a coordinate system. Let us have x-axis pointing to the east and y-axis pointing to the north. Let us also call the vector from A to B as AB, vector from B to C as BC, and the resulting vector from A to C as AC. As you know, the unit vector along the x-axis is i and along the y-axis is j.
AB = -200i
BC = -290cos27.5°i + 290sin27.5°j
Thus AC = AB + BC =
= (-290cos27.5° - 200)i + 290sin27.5°j
= ai + bj
So the distance |AC| = sqrt(a^2 + b^2)
and the direction of AC: arc tan (b/a)

All are in the following link:
http://answers.yahoo.com/question/index;_ylt=Ag.QJ7TENrj.C704iwni4hPty6IX;_ylv=3?qid=20070917171824AAkztmc&show=7#profile-info-gOs5HTOzaa

Answer 2

The answer is it is an acute triangle. Use the formula to find the answer.