The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65°E and the two towers are 30 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from Pine Knob and S 70°E from Colt Station. Find the distance of the fire from each tower.

The distance of fire from Pine Knob fire tower is 42.43 km

The distance of fire from Colt Station fire tower is 15.53 km

Step-by-step explanation:

Consider point A as Pine Knob fire tower and Point B as Colt Station fire tower. So the distance between both towers that is AB is 30 km.  

Now both fire tower  are located at a bearing of N65°E. That is at point A from north, Colt station fire tower is located at an angle of 65° towards east.

From ranger on Pine knob tower, fire spotted makes bearing of N80°E. That is at point A from north fire is located at an angle of 80° towards east.

Similarly, from ranger on Pine knob tower, fire spotted makes bearing of S70°E. That is at point B from south fire is located at an angle of 70° towards east.  

Now calculate and as follows,  

For

For

By using alternate angle property,

Refer attachment 1.  

From diagram consider the triangle ABC. To find the third angle that is \angle BAC can be calculated by using angle sum property of triangle.  

Refer attachment 2.  

Sine rule for the can be applied as follows,  

Substituting the values,

Now distance AC and BC can be calculated as follows,  

For distance AC,  

Cross multiplying,  

The distance of fire from Pine Knob fire tower is 42.43 km

For distance BC,  

Cross multiplying,  

The distance of fire from Pine Knob fire tower is 15.53 km

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step-by-step explanation: