SOLUTION: A hot air balloon is seen over Seven Springs simultaneously by two observers standing at two different points on the ground. ( The 2 people are facing each other and the balloon is

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Question 428216: A hot air balloon is seen over Seven Springs simultaneously by two observers standing at two different points on the ground. ( The 2 people are facing each other and the balloon is in between them in the air.) They are 1.75 miles apart on ground level. The angles of elevation are 33 degrees and 37 degrees respectively. How high above the ground is the balloon?
Answer by josmiceli(19441) (Show Source):
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Locate the point which is directly below the balloon. Call the point (C)
The person who sees the balloon at 37 degrees elevation
is looking higher, so that person is closer to the balloon.
Call their position (A)
Call the position of the other person (B)
Call the position of the balloon (D)
given:
AB = 1.75 miles
------------
= DC / AC
and, for the other person,
= DC / BC
------------
.7536 = DC / AC
.6494 = DC / BC
-------------
DC = .7536 x AC
DC = .6494 x BC
-------------
.7536 x AC = .6494 x BC
and
Since AB = AC + BC
1.75 = AC + BC
AC = 1.75 - BC
--------------
.7536 x (1.75 - BC) = .6494 x BC
Solve this for BC, then plug answer
back into .6494 = DC / BC
to get the height, DC