Triangulation Question: bearing, elevation angles from 2 observers

DoingMathMe

New member
Joined
Oct 28, 2017
Messages
5
Hi,

I am trying to solve this question and am having some difficultly.



Two observers 5 kilometers apart measure the bearing of the base of the balloon and the angle of elevation of the balloon at the same instant. One finds that the bearing is 041o, and the elevation is 24o. The other observer finds that the bearing is 032o, and the elevation is 26. 62o. Calculate the height of the balloon.



I am more interested in the working out rather than the final answer. Can anyone help?
 

Attachments

  • question1.jpg
    question1.jpg
    50.3 KB · Views: 2
Last edited by a moderator:
Two observers two kilometers apart measure the bearing of the base of the balloon and the angle of elevation of the balloon at the same instant. One finds that the bearing is 041o, and the elevation is 24o. The other observer finds that the bearing is 032o, and the elevation is 26. 62o. Calculate the height of the balloon.



I am more interested in the working out rather than the final answer. Can anyone help?
We're more interested in the process, too! So please reply with a clear listing of your thoughts and efforts so far, so we can "see" where you're getting stuck. Thank you! ;)
 
I think i have the right idea. That there are three triangles. The one created by the bearings(along the floor/ground) and two created by the elevations. I work out the edges of bearings triangle first. As it shares edges with the elevation triangles it helps me with figuring out the height of the balloon(which is a shared edge of the elevations triangles).

I think i use the law of sines first as i have a side(5km) and two angles (the bearings?). That gives me one of the edges of one of the elevation triangles. I then have an angle (elevation) and a side. So i can use sin/cos/tan, hypotenuse,opposite,adjacent.

here are some working outs

q3U8XP1.jpg
 
… One[observer] finds that the bearing is 041o …The other observer finds that the bearing is 032o
How has your class defined bearings?

The bearings shown in your first diagram use this convention: N41°E and N32°W.

When a bearing is given without compass designators (like 041° or 032°), it usually means that the initial ray of the angle points north (shown as broken, red lines below) and the terminal ray rotates in a clockwise direction.

bearings.JPG

Ignore the incorrect label (2 km).
 
Last edited:
I am not part of a class. I am working my way through a book in my spare time. Its called Trigonometry: A Complete Introduction.
It does not define bearings. My understanding is the same as yours. I am not sure how to work out the remaining angles. Build right-angled triangles that have the bearings as one angle?
[h=1][/h]
 
… I am working my way through a book … [it's] called Trigonometry: A Complete Introduction. It does not define bearings.
This book is not complete because it fails to define notation used within.


My understanding [of the given bearing notation] is the same as yours.
I don't understand this because your bearing diagram does not agree with mine.
 
The answer the book gives for this question is 2.23km but i dont get anywhere near that.
I have given up on this as i think the book is not clear enough.
 
Top