SOLUTION: Hi, I can't solve this word problem involving right triangles: "A surveyor finds that from point A on the ground the angle of elevation to the top of a mountain is 23degrees. Wh

Question 611188: Hi, I can't solve this word problem involving right triangles:
"A surveyor finds that from point A on the ground the angle of elevation to the top of a mountain is 23degrees. When he is at point B that is 1/4 mile closer to the base of the mountain, the angle of elevation is 43degrees. Assuming that the two points are on the same line, how high is the mountain?"
I don't know how to go about this problem, so if you could, please show and explain the steps as well. I would really appreciate it and it will help me keep up with our lessons. Thank you!
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You are being asked to compare 2 right triangles, both
of which have a side in common, which is the height.
At the surveyor's 1st position, call his distance from
the base of the mountain miles
Call the height of the mountain miles
-------------
(1)
and
(2)
------------------------
On my calculator,

--------------------
(1)
(1)
and
(2)
(2)
--------------------------
Substitute (1) into (2)
(2)
(2)
(2)
(2)
and, since
(1)
(1)
(1)
The mountain is miles high, or
ft high
check answer:
(1)
(1)
(1)
OK
(2)
(2)
(2)
(2)
Error is due to rounding off
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