Use a special right triangle to write tan 60° as a fraction
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Answer:
29.5 m 64° west of north
Step-by-step explanation:
A suitable vector calculator can add the vectors for you. (See attached.) Here, we have used North as the 0° reference and positive angles in the clockwise direction (as bearings are measured).
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You can also use a triangle solver (provided by many graphing calculators and stand-alone apps). For this, and for manual calculation (below) it is useful to realize the angle difference between the travel directions is 70°.
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Using the Law of Cosines to find the distance from start (d), we have (in meters) ...
d² = 28.6² + 22² -2·28.6·22·cos(70°) ≈ 871.561
d ≈ √871.561 ≈ 29.52 . . . . meters
The internal angle between the initial travel direction and the direction to the end point is found using the Law of Sines:
sin(angle)/22 = sin(70°)/29.52
angle = arcsin(22/29.52×sin(70°)) ≈ 44.44°
This angle is the additional angle the destination is west of the initial travel direction, so is ...
20° west of north + 44.44° farther west of north = 64.44° west of north
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In the second attachment, North is to the right, and West is down. This is essentially a reflection across the line y=x of the usual map directions and angles. Reflection doesn't change lengths or angles, so the computations are valid regardless of how you assign map directions to x-y coordinates.
