How Far is the Ship from the Rocks When Sighting a Lighthouse?

[cphill29]

Homework Statement

A lighthouse that rises 49 ft above the surface of the water sits on a rocky cliff that extends 19 feet from its base. A sailor on the deck of a ship sights the top of the lighthouse at an angle of 30 degrees above the horizontal. If the sailor's eye level is 14 ft above the surface of the water, how far is the ship from the rocks?

Homework Equations

tanx=opp/adj

The Attempt at a Solution

tan30=35/x
xtan30=35
x=35/(tan30)
x=60.6 ft

Since the lighthouse is 49 feet above the surface and the sailor is 14 feet above the surface, the opposite side of the triangle is 35 feet, but I can't get the right answer doing this.

 

[PhanthomJay]

The wording of the problem is not that clear. I believe when saying that ' the rock cliff extends 19 feet from its base ' , that it means that the rocks start 19 feet horizontally away the lighthouse. So your method is correct, just make the necessary adjustment to your answer.

 

[cphill29]

The wording of the problem is not that clear. I believe when saying that ' the rock cliff extends 19 feet from its base ' , that it means that the rocks start 19 feet horizontally away the lighthouse. So your method is correct, just make the necessary adjustment to your answer.

That's what I thought, too, but it gives me a picture and it's clear that is not the case. I did try it though and still got the answer wrong.

 

[PhanthomJay]

What does the pic show??

 

[Nickie]

Your attempt at solving this problem is correct. However, there may be a slight error in your calculations. The correct value for x would be approximately 60.6 feet, as you have stated. It is possible that the discrepancy in your answer may be due to rounding errors. Calculating with more decimal places can help to get a more accurate answer. Additionally, it is important to label your variables clearly and use appropriate units in your calculations. Overall, your use of trigonometry and vectors in this problem is correct and demonstrates a good understanding of these concepts. Keep up the good work!