SOLUTION: This is a word problem and I'm using Sin,Cos, and Tan so I'm pretty sure it has something to do with that. From a 60foot observation tower on the coast, a Coast Guard officer sig

Algebra ->  Trigonometry-basics -> SOLUTION: This is a word problem and I'm using Sin,Cos, and Tan so I'm pretty sure it has something to do with that. From a 60foot observation tower on the coast, a Coast Guard officer sig      Log On


   



Question 211660This question is from textbook Trigonometry
: This is a word problem and I'm using Sin,Cos, and Tan so I'm pretty sure it has something to do with that.
From a 60foot observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression of the boat is 3degrees. How far is the boat from the shoreline??
This question is from textbook Trigonometry

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!



To show the angle of depression, draw
a horizontal line at the top of the tower:



The angle between that horizontal and the 
line of sight to the boat is 3°



Now by alternate interior angles the angle in the right
corner of the triangle is also 3°



Now 60 is the opposite side to the angle 3° 
at the bottom right corner, and x is the adjacent side.

So we know to use tangent

tan(3°) = 60%2Fx

Multiply both sides by x

x*tan(3°) = 60

x = 60%2Ftan%28%223%B0%22%29

x = 1144.868201

or about 1145 feet.

Edwin