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

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2 Answers
Feb 15, 2018

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?

Feb 15, 2018

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