Question 428216
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
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{{{ tan(37)}}} = DC / AC
and, for the other person,
{{{ tan(33)}}} = DC / BC
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 .7536  = DC / AC
 .6494  = DC / BC
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DC = .7536 x AC
DC = .6494 x BC
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.7536 x AC = .6494 x BC
and
Since AB = AC + BC
1.75 = AC + BC
AC = 1.75 - BC
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.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