Lighthouse?

Question

A lighthouse that rises h=52 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 teh lighthouse at an angle of 31.0 degress above teh horizontal. If the sialor's eye level is 14 ft above the water, how far is the ship from the rocks?

Answer 1

ok,  the sailors rule of thumb is that the curvature of the earth equals 6 feet for every 10 miles.

so if the lighthouse is 52 feet and the sailor is 14 foot then the total is 66 feet. or 110 miles out from the light house.  =580800 ft

tothe rocks is 19 feet closer or 580781 ft

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Answer 2

Yeah, study more...

okay, even up the heights...the sailor is at 14ft so lets make him and the base of the lighthouse plus cliff equal.

19-14=5...add this to the overall height for the apex of the triangle...52+5=57

In other words, the top of the lighthouse is 57ft above the elevation of the sailor.

Draw a verticle line on paper to scale representing 57ft.

From the base draw a scaled line along horizontally to the edge of the paper. This is the base of your triangle and will be your distance line.

Now, with your protractor set at the top of the 57ft  vertical line(the lighthouse top) draw an angle of 31 degrees and connect to the base line. Where the extended angle connects at the base is the position of the sailor. Measure from the lighthouse base to to the intersect to arrive at the distance.

Simple...good luck.

Answer 3

Having homework troubles?  Study harder...lol.

Answer 4

Its just a triangle with one adjustable leg.(31.deg.)

Answer 5

The Table will straightaway give you the answer! (trigonometry can be fun!)

Answer 6

far enough to maneuver around the rocks