Station A is located 18 miles due east of Station B The bear

Station A is located 18 miles due east of Station B. The bearing of a fire from A is S 10 degrees E and the bearing of the fire from B is S 42 degree E Determine the distance from the fire to B to the nearest hundredth of a mile. draw a map.

Solution

First you need to plot or draw the diagram using the given data in your question. Use a the N, E, W & S quadrants in order to plot exactly the given bearings.

After plotting, the diagram shows a triangle with points A, B & F (for Fire). The included angles respectively are : Angle A = 98 deg. & 50\' ; Angle B = 61 deg. & 40\' and Angle F = 19 deg. 30\'

Angle A = 90 deg + 10 deg. = 100 deg.
Angle B = 90 deg - 42 deg. = 48 deg
Angle F = 180 deg - Ange A - Angle B
Angle F = 180 - (100+48) = 32

Distance AB = 18 miles
Distance BF = (distance of fire to B) = ?

By Sine Law :
AB/Sine F = BF/Sine A
BF = (AB x Sine A)/Sine F
BF = (18x Sine 100 deg. )/(Sine 32 deg)
BF = 3.345 miles
say 3.300 miles (Answer)