
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 23rd, 2017, 10:32 PM  #1 
Senior Member Joined: Apr 2008 Posts: 175 Thanks: 3  How do you solve this bearing problem?
From the top of a 50m observation tower, a fire ranger observes smoke in two locations. One is on a bearing of 40 degrees with an angle of depression of 8 degrees and the other is on a bearing of 205 degrees with an angle of depression of 13 degrees. How far apart are the sources of smoke? I am very confused about how to incorporate bearings into trigonometry. Please help me. Thanks a lot. 
June 23rd, 2017, 11:22 PM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,264 Thanks: 650 
can you assume that the fires both occur at altitude 0m?

June 24th, 2017, 05:00 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,569 Thanks: 1272 
Assuming both fires have the same vertical elevation as the base of the tower ... The horizontal distance from the base of the tower to the first fire is $d_1=\dfrac{50}{\tan(8^\circ)}$ The horizontal distance from the base of the tower to the second fire is $d_2=\dfrac{50}{\tan(13^\circ)}$ the angle between their respective bearings is $205^\circ  40^\circ =165^\circ$ distance between the two fires, $D = \sqrt{d_1^2+d_2^2 2d_1d_2\cos(165^\circ)}$ 
July 2nd, 2017, 12:08 AM  #4 
Senior Member Joined: Apr 2008 Posts: 175 Thanks: 3 
Thanks a lot, skeeter.


Tags 
bearing, problem, solve 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Cylinder Bearing Problem  pikerman  Geometry  3  February 15th, 2015 11:34 AM 
Complex coordinate bearing calculation problem, need help…  TheSwede  Algebra  0  January 10th, 2014 12:05 PM 
Bearing Trigonometry Problem  shiseonji  Trigonometry  3  July 28th, 2013 01:43 AM 
plane + wind bearing problem  triplekite  Algebra  7  October 8th, 2012 11:29 PM 
plane + wind bearing problem  triplekite  Linear Algebra  0  January 1st, 1970 12:00 AM 