A fire is sighted due west of lookout A The bearing of the f

A fire is sighted due west of lookout A. The bearing of the fire from lookout B, 14.2 mi due south of A, is N 46.5 Degree W. How far is the fire from B, rounded to one decimal place? A right triangle with a flame on the westmost point, A directly east of the flame, and B directly south of A. e icon due to Nemo, Pixabay, released under Public Domain CCO4/12/2012 http://pixabay.com/en/fi camp-bonfire-wood- heat-30231/20.6 mi 21.6 mi 22.6 mi 23.6 mi

Solution

You can use the law of sine. The fire, lookout A and B are forming a triangle and their interior angles add up to 180. A is 90, B is 46.5 and F will be 43.5. The distance from A to B is 14.2.

Thus, sin(43.5) / 14.2 = sin(90) / x where x is the distance between the fire and B.
If you draw a diagram, you will see 14.2 is opposite of the angle 43.5. Likewise, x is opposite of the angle 90. The law of sine says that the ratio will be the same.
x = 20.6