A person sitting on a boat is situated 2 metres above sea level. He has a device for measuring angles and notes that a straightline from himself to the top most point of a nearby lighthouse makes an angle of 16 degrees wuth the horizontal. After travelling a further 50m from the lighthouse this angle has decreased to 12 degrees.
How high is the top most point of the lighthouse above sea level (asssuming no triangles are right angled)?
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Let the height of light house above the the sitting man is x meters. Then the height of light house above sea level = x+2
The horizontal distance between ligh house and man = y
So for first angle;
tan (16) = x/y----------------(1)
For second angle;
tan (12) = x/(y+50)------------(2)
tan (16)/tan (12) = (x/y)/(x/(y+50)
0.287/0.213 = (y+50)/y
By solving this you can get y = 143.2 m
Form (1) tan (16) = x/y
0.287 = x/143.2
x = 41.06
Then the height of light house;
The horizontal line of sight of the man is 2m above sea level.
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