SOLUTION: the distance from you to the base of a tower on top of a hill is 2760 ft. the angle of elevation of the base is 26 degrees the angle of elevation of the top of the tower is 32 degr

Algebra ->  Trigonometry-basics -> SOLUTION: the distance from you to the base of a tower on top of a hill is 2760 ft. the angle of elevation of the base is 26 degrees the angle of elevation of the top of the tower is 32 degr      Log On


   

Question 1117065: the distance from you to the base of a tower on top of a hill is 2760 ft. the angle of elevation of the base is 26 degrees the angle of elevation of the top of the tower is 32 degrees.find the nearest foot the height of the tower above the top of the hill
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the distance from you to the base of a tower on top of a hill is 2760 ft. the angle of elevation of the base is 26 degrees the angle of elevation of the top of the tower is 32 degrees.find the nearest foot the height of the tower above the top of the hill
Equations::
hill = 2760*tan(26) = 1356.14 ft
tower + hill = 2760*tan(32) = 1724.64 ft
----
Ans:: tower = 1724.64-1356.14 = 368.5 ft
-----
Cheers,
Stan H

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
this is my diagram of the problem as i see it.

the base of the tower on the hill is at point D.

the top of the tower on the hill is at point A.

the angle of elevation from the ground to the base of the tower is angle DBC which is 26 degrees.

the angle of elevation from the ground to the top of the tower is angle ABC which is 32 degrees.

you are at point B.

the distance from point B to point D is equal to 2760 feet which is the length of line segment DB.

triangle DCB and triangle ACB are both right triangles.

cosine (DBC) is equal to adj/hyp = CB / DB.
solve for CB to get CB = DB * cosine (DBC).
this becomes CB = 2760 * cosine (26).
this makes CB = 2480.671568.

sine (DBC) is equal to opp/hyp = DC / DB.
solve for DC to get DC = DB * sine (DBC).
this becomes DC = 2760 *I sine (26).
this makes DC = 1209.904365.

cosine (ABC) = adj/hyp = CB / AB.
solve for AB to get AB = CB / cosine (ABC).
this becomes AB = 2480.671568 / cosine (32).
this makes AB = 2925.154339.

sine (ABC) = opp/hyp = AC / AB.
solve for AC to get AC = AB * sine (ABC).
this becomes AC = 2925.154339 * sine (32).
this makes AC = 1550.095635.

AD = AC - DC = 1550.095635 - 1209.904265 = 340.19127.

that's the height of the tower that's sitting on the top of the hill.

round that to the nearest foot to get 340 feet.

here's my diagram.

$$$