SOLUTION: from the top of a cliff the angles of depression of two boats in the same vertical plane at the observer's eyes are 30 E and 45. if the distance between the boats is 100 feet, find
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Question 1058385: from the top of a cliff the angles of depression of two boats in the same vertical plane at the observer's eyes are 30 E and 45. if the distance between the boats is 100 feet, find the height of the cliff Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! Draw this and the angle from the boat to the cliff is 30 degrees.
The other boat has an angle of 45 degrees.
The cliff height is x
the distance to the first boat is y, to the second boat y+100
tangent 30=x/(y+100)
tangent 45=x/y
Therefore, y=x, since tan 45=1
sqrt(3)/3=x/(x+100) substituting and knowing tan 30 is sqrt (3)/3
0.5774(x+100)=x
0.5774x+57.74=x
57.74=0.4226 x
dividing out
136.63 or 136 feet.
