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?
 👍
 👎
 👁
 ℹ️
 🚩
2 answers

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 👍
 👎
 ℹ️
 🚩

The captain of a ship at sea sights a lighthouse which is 160 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 17 °. How far is the ship from the base of the lighthouse?
 👍
 👎
 ℹ️
 🚩
Answer this Question
Related Questions

Calc
A lighthouse is fixed 130 feet from a straight shoreline. A spotlight revolves at a rate of 11 revolutions per minute, (22 rad/min ), shining a spot along the shoreline as it spins. At what rate is the spot moving when it is along the shoreline 12 feet

physics
A lighthouse that rises 49 ft above the surface of the water sits on a rocky cliff that extends 19 ft from its base. A sailor on the deck of a ship sights the top of the lighthouse at an angle of 30.0 ∘ above the horizontal. If the sailor's eye level is

math
can you please check my work. A scientist uses a submarine to study ocean life. She begins at sea level, which is at an elevation of 0 ft. she travels straight down at a speed of 3.5ft per second. she then travels directly up 30seconds at a speed of 2.2ft

Math
A LIGHTHOUSE IS 10 MILES NORTHEAST OF A DOCK. A SHIP LEAVES THE DOCK AT NOON,AND SAILS EAST AT A SPEED OF 12 MILES AN HOUR. AT WHAT TIME WILL IT BE 8 MILES FROM THE LIGHTHOUSE?

Mathematics
Two boats 70 metres apart are on opposite side of a lighthouse from the two boats are 71.6° and 45°.Find the height of the lighthouse (tan 71.6°=3)

Math Data Management
In how many ways can the 12 members of a volleyball team line up, if the captain and assistsant captain must remain together? Thank you in advance.

flag pole, math, geometry, urgent
A palm tree that is 32 feet tall, casts a shadow that is 26 feet long. Matt is 6 feet tall and standing near the palm tree. Use the figure above to determine the length of Matt’s shadow. Round to the nearest tenth.

pre algebra
If a sail of a ship is 10 feet long and has a diagonal length of 26 feet, what is the height of the sail in feet? A 29 B 24********** C 17 D 8

Math
the elevation of a sunken ship is 120 feet. your elevation is 5/8 of the ship's elevation. what is your elevation?

core mathematics
Two boats are 70m and on opposite sides of a lighthouse.from the two boats,the angles of elevation of the lighthouse are 71 and 45 respectively.find the height of the lighthouse.

Calculus
At noon, ship A is 130 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?

CALCULUS
At noon, ship A is 130 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?

word problem math
Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Dixon's shadow is 18 feet long and Ariadne's shadow is 15 feet long. If Dixon is 6 feet tall, how tall is Ariadne?

Math
The king's ship sank with 8 gold bars aboard. The king paid captain nemo 4/5 of one bar for finding the gold. The captain gave 1/2 of his gold to charity. What fraction of a bar went to charity?

math
If a tree is 10 feet tall after two years and 25 feet tall after 5 years, find the rate of change of growth of the tree if y is the height in feet and x is the number of years. Be sure to give correct units.

math
find the difference of an elevation of 30 feet below sea level and an elevation of 118 feet above sea level ans.. 30  118 = 148

Precalculus
1. A man stands 12 feet from a statue. The angle of elevation from the eye level to the top of the statue is 30 degrees, and the angle of depression to the base of the statue is 15. How tall in the statue? 2. Two boats lie on a straight line with the base

math
At a given time, the height of an object is directly proportional to the length of the shadow that is cast on the ground. A person 6 feet tall casts a shadow 1 foot long at noon. a) What is the length of the shadow cast by a flagpole known to be 20 feet

English (Check)
Read the following excerpt from Equiano's autobiography. Then answer the questions below. Some of the people of the ship used to tell me they were going to carry me back to my own country and this made me very happy. I was quite rejoiced at the sound of

math
Q. The rectangularshaped doctor's office has an area of 120 square feet and a perimeter of 44 feet. What are the dimensions of this office space?  A. Do I add just add 120 by 44??
Still need help?
You can ask a new question or browse existing questions.