Word Problem on Sine Rule

Topic : Sine Rule

Question : Lookout station B is located 7 miles due east of station A. The bearing of a fire from A is S 8degree50’ W and the bearing from B is S 28degree20’ W. Determine the distance from the fire to B(to the nearest tenth of a mile)

Solution :

Figure is as shown in the figure according the question

From Sine Rule

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

a = c Sin A / Sin C
a = 7 * Sin (90º + 8º 50’) / Sin (90º - 28º 20’)
a = 7 * Sin (98º 50’) / Sin (19º 30’)
a = 20.72miles