SOLUTION: From a point on a level plain the angle of elevation of the top of the hill is 23° 46', and a tower 45m high standing on top of the hill subtends an angle of 5° 16'. Find the hei

Algebra ->  Trigonometry-basics -> SOLUTION: From a point on a level plain the angle of elevation of the top of the hill is 23° 46', and a tower 45m high standing on top of the hill subtends an angle of 5° 16'. Find the hei      Log On


   



Question 1204103: From a point on a level plain the angle of elevation of the top of the hill is 23° 46', and a tower 45m high standing on top of the hill subtends an angle of 5° 16'. Find the height of the hill.
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
If bottom angle 23° 46' is measure B
and top angle 5° 16' is measure T
(The assigning B and the T very helpful because too many characters to write or type before finishing!)
x, length from point to bottom at center of hill
y, the height of hill

Then when you draw and label the description, you may make these:

system%28y%2Fx=tan%28B%29%2Ctan%28T%2BB%29=%28y%2B45%29%2Fx%29

...and solve....

On the way find y=%2845tan%28B%29%29%2F%28tan%28T%2BB%29-tan%28B%29%29;
Now, substitute and evaluate y.