SOLUTION: the chinese used a way of measuring heighth of a mountin by viewing it from 2 diffrent locations and counculating the angle from where thay were to the top of the mountain. the

Question 32413: the chinese used a way of measuring heighth of a mountin by viewing it from 2 diffrent locations and counculating the angle from where thay were to the top of the mountain. the frist angle measure was 8.7� and the 2nd was 7.5�. the two angles were measured from 18,325 feet apart. how tall is the mountain?
Found 2 solutions by venugopalramana, rfadrogane:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
the chinese used a way of measuring heighth of a mountin by viewing it from 2 diffrent locations and counculating the angle from where thay were to the top of the mountain. the frist angle measure was 8.7� and the 2nd was 7.5�. the two angles were measured from 18,325 feet apart. how tall is the mountain?
LET BT BE THE MOUNTAIN,B BEING THE BOTTOM ON THE GROUND AND AND T THE TOP.
LET THE MAN ON THE GROUND VIEWING THE MOUNTAIN BE AT P FIRST ,SEEING AT AN ANGLE OF ELEVATION OF 8.7 DEG..LET HIM MOVE AWAY FROM THE MOUNTAIN FROM P TO Q ON THE GROUND FROM WHERE THE ANGLE OF ELEVATION IS 7.5 DEG.PQ=18325 FT.
SO IN RIGHT ANGLE TRIANGLE PBT,
BT=H...HEIGHT OF MOUNTAIN
TAN(BPT)=TAN(8.7)=BT/PB=H/PB...OR...PB = H/TAN(8.7)=H*COT(8.7)
IN RIGHT TRIANGLE QBT
BT=H
TAN(BQT)=TAN(7.5)=BT/QB=H/QB...OR...QB = H/TAN(7.5)=H*COT(7.5)
PQ=18325=QB-PB=H*COT(7.5)-H*COT(8.2)=H*{COT(7.5)-COT(8.2)}
H=18325/{COT(7.5)-COT(8.2)}=
=27910.4 FT.

Answer by rfadrogane(214) (Show Source): You can put this solution on YOUR website!
h(cot 7.5 deg - cot 8.7 deg) = 18,325
h = 18,325/(cot 7.5 deg - cot 8.7 deg.)
h = 17,275.92 ft.---ans..
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