Question

Trigonometry bearings confuses me. I only solved right and obtuse triangles using pythagorean, sines and cosines laws?

Answer 1

Please see below.

Explanation:

What are we trying to find?

How far west of the origin she is.

What is the in the picture?

The length of the line segment from Origin to A
Which is one leg of a right triangle.

I only know one side, so I can't use the Pythagorean Theorem.

Do I know the non-right angles?

After I figure those out, can I find the unknown?

Answer 2

She is `10m` west of her starting point.

Explanation:

There is a difference between 'west' and 'due west.

All bearings between 180° and 360° are west of (meaning on the 'western (ie left) side of) the NS line and all bearings between 000° and 180° are east of (meaning on the eastern side )of the NS line. Due west means directly west (on a bearing of 270°)

Let's refer to the intersection of the NS and EW line `C` - the middle of the compass,

The required distance is `AC`

In `Delta BAC, hatB = 90°, CB = 20m and BhatCA = 60°`

`BhatCA = 300°-270° =60°`

Use trig to find the length of `AC`

`(AC)/20 = cos60°`

`AC = 20cos 60°`

`AC = 10m`