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 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
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 Originally Posted by koolie Can someone please draw the diagram for that question and post it here?
You want him to search the diagram for a question he asked 3 years ago to post it here for no reason?

 February 16th, 2019, 04:15 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,484 Thanks: 2041 The third triangle that Country Boy described doesn't have a right angle, but is otherwise correctly described.

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### 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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