SOLUTION: From the top of a vertical cliff 68 metres high, an observer notices a yacht at sea. The angle of depression to the yacht is 47 degrees. The yacht sails directly away from the cli

Question 858224: From the top of a vertical cliff 68 metres high, an observer notices a yacht at sea.
The angle of depression to the yacht is 47 degrees. The yacht sails directly away from the cliff,
and after 10 minutes the angle of depression is 15 degrees. How fast does the yacht sail?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
height of tower = 68m
angle of depression = 47 deg
angle of depression after 10 minutes = 15 deg
10 min = 600 seconds
Let the initial ground distance from tower to yacht x m
Tan 47 = 68/x
x= 68/tan 47
Let the speed of the yacht = y
distance traveled in 600 seconds = 600y
Tan 15 = 68/(x+600y)
x+600y = 68/tan 15
x= (68/tan 15)-600y
68/tan47 = (68/tan 15)-600y
600y = (68/tan 15)- (68/tan 47)
600y=253.8-63.4
y=0.32 m/s------ speed of the yacht
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