Two fire-lookout stations are 16 miles apart, with station B directly east of station A. Both stations spot a fire. The bearing of the fire from station A is N35°E

Question

and the bearing of the fire from station B is N30°W. How far, to the nearest tenth of a mile, is the fire from each lookout station?

Answer 1

Elle

Suppose the fire is at point C. Then you can draw a triangle ABC. AB is horizontal, distance 16.

The angle A must be 65 degrees and the angle B must be 60 degrees. (using the two bearings given).

So angle C must be 180 - 65 - 60 = 55 degrees.

You need the length of AC (b) and BC (a) . Use the sine rule. You know c = 16

a/sin A = b/sin B = c/sin C

You know c, and can find sin C. Then just use this to find a, b. (a should be 17.7, b 16.9. Use exact values in your calculator eg to find a, type in (16*sin(65)/sin(55))

Mike