The answer to the math question
A lighthouse keeper has a 10º angle of depression between the horizontal light beam and the line of sight from the ship. If the
keeper is 19 m above water, how far is the ship from the base of the lighthouse?
2 answers:
The image I provided is a good diagram of the situation.
The keeper is 19 meters above the water.
He is looking down at a ship at a 10° angle from the horizon.
We want to find the distance between the base of the lighthouse and the ship.
The side we are trying to find is opposite the angle 10°. The lighthouse is adjacent to the angle 10°.
Therefore, we can use the tangent function (opposite over adjacent).
tan 10° = x/19
Multiply both sides by 19:
19 tan 10° = x
Solve using a calculator:
x = 3.350 meters
The ship is 3.350 meters from the lighthouse.
The keeper is 19 meters above the water.
He is looking down at a ship at a 10° angle from the horizon.
We want to find the distance between the base of the lighthouse and the ship.
The side we are trying to find is opposite the angle 10°. The lighthouse is adjacent to the angle 10°.
Therefore, we can use the tangent function (opposite over adjacent).
tan 10° = x/19
Multiply both sides by 19:
19 tan 10° = x
Solve using a calculator:
x = 3.350 meters
The ship is 3.350 meters from the lighthouse.
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