What is the distance and direction between city A and city C?

[hrgardner33]

Homework Statement

An airplane flies 200 km due west from city A to city B and then 345 km in the direction of 34.5° north of west from city B to city C. In straight-line distance, how far is city C from city A? Relative to city A, in what direction is city C?

Homework Equations

The Pythagorean theorem

The Attempt at a Solution

398.78 km

 

[gerben]

The Pythagorean theorem is about right-angled triangles. The triangle ABC in your problem is not right-angled.

The way to solve this would be: draw the situation, then try to make some right-angled triangle, calculate the length of its sides using sine and cosine functions and then use the Pythagorean theorem.

 

[hrgardner33]

I don't know how to draw 34.5 degrees north of west.

 

[gerben]

Yeah I can understand that, I do not find it very clear terminology either, but I am assuming they meant rotating the negative x-axis (i.e. west) 34.5 degrees in clockwise direction (i.e. towards north).