Make your sketch, label the person nearest the obelisk as A and the person's position as B
Top of obelisk as P and its bottom as Q.
Look at triangle PAB
angle B = 44
angle PAB = 180-65 = 115
then angle APB = 21
by the sine law:
AP/sin44 = 25/sin21
AP = 25sin44/sin21
In the right-angled triangle PQA
sin 65 = PQ/AP
PQ = APsin65
= (25sin44/sin21)sin65
= ....
you do the buttonpushing
Another way would be the way Steve did it in
http://www.jiskha.com/display.cgi?id=1358888863
Two people decide to find the height of an obelisk. They position themselves 25 feet apart in line with, and on the same side of, the obelisk. If they find that the angles of elevation from the ground where they are standing to the top of the obelisk are 65 degrees and 44 degrees, how tall is the obelisk?
2 answers
If the nearer observer is at distance x from the obelisk, then we have
h/x = tan 65°
h/(x+25) = tan 44°
so, eliminating x, just solve for h in
h/tan65° = h/tan44° - 25
h = 25/(cot44°-cot65°)
h/x = tan 65°
h/(x+25) = tan 44°
so, eliminating x, just solve for h in
h/tan65° = h/tan44° - 25
h = 25/(cot44°-cot65°)