February 10th, 2016, 01:28 AM  #1 
Newbie Joined: Feb 2016 From: straya Posts: 2 Thanks: 0  Worded question
Worded question that I have no idea how to answer  Points A B and C all lie on the same horizontal ground with B due north of A and C on a bearing of 030* from A. From the top of a vertical tower at A, 37 metres above ground, point B has an angle of depression of 17* and point C has an angle of depression of 12*. How far is B from C? Last edited by skipjack; February 16th, 2019 at 04:02 AM. 
February 10th, 2016, 05:01 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
There are three triangles of importance here. One is the right triangle formed by the tower at A, the line from A to B, and the line of sight from the top of the tower to B. If we let "x" be the distance from A to B then x/37= tan(17). That's easy to solve for x. Another is the right triangle formed by the tower at A, the line from A to C, and the line of sight from the top of the tower to C. If we let "y" be the distance from A to C, then y/37= tan(12). That's easy to solve for y. The third triangle is the right triangle formed by the lines from A to B, from A to C, and from B to C. Call the distance from B to C "z". By the "cosine law" $\displaystyle z^2= x^2+ y^2 2xy \cos(30^\circ)$. Last edited by skipjack; February 16th, 2019 at 04:04 AM. 
February 12th, 2016, 12:39 AM  #3 
Newbie Joined: Feb 2016 From: straya Posts: 2 Thanks: 0 
Thank you. :d
Last edited by skipjack; February 16th, 2019 at 04:05 AM. 
February 15th, 2019, 07:30 PM  #4 
Newbie Joined: Feb 2019 From: Australia Posts: 1 Thanks: 0 
Can someone please draw the diagram for that question and post it here?

February 15th, 2019, 10:53 PM  #5 
Senior Member Joined: Oct 2009 Posts: 803 Thanks: 301  
February 16th, 2019, 04:15 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,751 Thanks: 2135 
The third triangle that Country Boy described doesn't have a right angle, but is otherwise correctly described.


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a b and c are points on horizontal ground b is due north,a light string of length a is connected to two points on the same horizontal ground show that T =w(a² b²)/2a²
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