# Trigonometry

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Surveying
A surveyor wishes to find the distance across a swamp. The bearing from A to B (Segment AB is opposite side of triangle) is N 32° W. The surveyor walks 50 meters from A to C, and at the point C the bearing to B is N 68° W. (Segment AC is adjacent side of triangle & Segment BC is hypotenuse side of triangle.)

A) Find bearing from A to C?
B) What is the distance from A to B?

• Trigonometry -

Confusing description. Where does the swamp come in ?
After a few tries I got a right-angled triangle with angle A = 90°
I sketched a vertical line AP .
From your description, angle BAP = 32°, leaving
angle PAC = 58°
I also drew a vertical from C to Q
so that angle QCB = 68°

let angle BCA = Ø
since AP and CQ are parallel
angle PAC + angle ACQ = 180°
58 + Ø+68=180
Ø = 54°

OK then....

A) bearing from A to C is N 58° E
B) tan 54° = AB/50
AB = 50tan54 = 68.82 m

• Trigonometry -

Reiny thanks a lot for the help! I welcome you with a nice smile! Here is the website where I can show how the problems look/appear like...

4.8 applications and models Comcast

Click the first result that appears on the web search page.
Go to page 8 in the PDF document on problem #33.

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