Question 197659: a) As shown in the diagram, a ship at sea is sighted from the top of a 60-foot lighthouse. If the angle of depression of the ship from the top of the lighthouse measures is 15 degree, find to the nearest foot, how far the ship is from the base of the light house.
b) In right triangle DEF, the measure of angle E is 90 degree, the length of side EF is 7 centimeters, and the length of side DF is 12 centimeters. Find the measure of angle F to the nearest degree.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a) As shown in the diagram, a ship at sea is sighted from the top of a 60-foot lighthouse. If the angle of depression of the ship from the top of the lighthouse measures is 15 degree, find to the nearest foot, how far the ship is from the base of the light house.
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Draw the picture.
The angle of depression from the lighthouse to the ship is the same as
the angle of elevation from the ship to the top of the lighthouse.
Equation:
tan(15 degrees) = 60/base
base = 60/tan(15) = 223.92 ft.
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b) In right triangle DEF, the measure of angle E is 90 degree, the length of side EF is 7 centimeters, and the length of side DF is 12 centimeters. Find the measure of angle F to the nearest degree.
Draw the picture:
F = arctan(12/7) = 59.74 degrees
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Cheers,
Stan H.
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