Question 1207648: Hi, can you please help me solve this problem? Thank you.
A surveyor wishes to find the distance between two inaccessible points A and B. As shown in the figure, two points C and D are selected from which it is possible to view both A and B. The distance CD and the angles ACD, ACB, BDC, and BDA are then measured. If CD=120~ft, ∠ACD=115°, ∠ACB=92°, ∠BDC=125°, and ∠BDA=100°, approximate the distance AB.
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
Here's the drawing, approximately but not exactly to scale.
This is a law of sines and cosines problem. I'm not going to finish it for you.
These aren't special angles, so you're going to have a lots of long decimals.
The more you round off, the less accurate your answer will be.
By subtracting I found the two angles in green.
You have angle-side-angle in triangle CED, so use the law of sines to solve for
the other 3 parts of triangle CED.
Then, by subtracting angles find the two acute angles at E.
Then you will have angle-side-angle in each of the triangles ACE and BED,
so use the law of sines on triangle ACE to find AE, then again on triangle
BED to find BE.
Then for triangle AEB, you will have side-angle-side. That will be
AE, angle AEB (same as angle CED), and BE.
and you can then find AB, using the law of cosines on triangle AEB.
Happy solving!
Edwin
Answer by math_tutor2020(3816)  (Show Source):
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