trig
posted by Dan .
The captain of a ship at sea sights a lighthouse which is 120 feet tall.
The captain measures the the angle of elevation to the top of the lighthouse to be 19 ^\circ.
How far is the ship from the base of the lighthouse?

H = Hight of lighthouse
L = Distance between a ship and a lighthouse
tan( theta ) = H / L
If 19^ mean 19° then:
tan( theta ) = H / L
tan( 19° ) = 120 / L
L * tan( 19° ) = 120 Divide both sides with tan( 19° )
L = 120 / tan ( 19° )
L = 120 / 0.34433
L = 348.5 ft
If 19^ mean 19´ then:
tan( theta ) = H / L
tan( 19´ ) = 120 / L
L * tan( 19´ ) = 120 Divide both sides with tan( 19´ )
L = 120 / tan ( 19´ )
L = 120 / 0.00553
L = 21,699.82 ft
If 19^ mean 19" then:
tan( theta ) = H / L
tan( 19" ) = 120 / L
L * tan( 19" ) = 120 Divide both sides with tan( 19" )
L = 120 / tan ( 19" )
L = 120 / 0.00009
L = 1,333,333.33 ft
Respond to this Question
Similar Questions

trig
The captain of a ship at sea sights a lighthouse which is 280 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 25. How far is the ship from the base of the lighthouse? 
mathgeometry
a person in a boat sights the top of a lighthouse at an angle of elevation of 20 degrees. if the lighthouse is 40 feet tall find the distance from the base of the lighthouse to the boat. 
Calculus
The captain of a ship at sea sights a lighthouse which is 260 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 21. How far is the ship from the base of the lighthouse? 
geometry
Daniel sees a lighthouse in the harbor. He estimates the angle of elevation is 60°. If the lighthouse is 120 feet tall, what is the approximate distance between Daniel and the top of the lighthouse? 
Geometry
how do I set up this problem a man standing on the deck of a ship with his eyes 25 feet above sea level notes that the angle of elevation to the top of a 25 foot lighthouse is 3 degrees 27 minutes. how far is the boat from the lighthouse 
Maths
An observer at the top of a lighthouse 55m Hugh sights a ship at a sea angle of depression of 18°. If the foot of the lighthouse is at sea level how far is the ship from the foot of the light house 
Geometrt
Casey sights the top of an 84 foot tall lighthouse at an angle of elevation of 58 degrees. If casey is 6 feet tall, how far is he standing from the base of the lighthouse? 
GEOMETRY
cASEY SIGHTS THE TOP OF AN 84 FOOT TALL LIGHTHOUSE AT AN ANGLE OF ELEVATION OF 58 DEGREE. IF CASEY IS 6 FEET TALL, HOW FAR IS HE STANDING FROM THE BASE OF THE LIGHTHOUSE. I DO NOT UNDERSTAND WHAT IS ANGLE OF ELEVATION CAN YOU SHOW … 
Trigonometry
John stands on top of a little lighthouse looking out at a nearby tall lighthouse that is 200 feet away. He looks at the top of the tall lighthouse with a 3 degree angle of elevation, but looks at the bottom of the tall lighthouse … 
Geometry
Casey sights the top of an 84 foot tall lighthouse at an angle of elevation of 58 degrees. If Casey is 6 feet tall, how far is he standing from the base of the lighthouse?