Question

A lighthouse that rises h1 = 47.0 ft above the surface of the water sits on a rocky cliff that extends d = 17.4 ft from its base, as shown in the figure below.
A sailor on the deck of a ship sights the top of the lighthouse at an angle of theta = 29.3 degree above the horizontal. If the sailor's eye level is h2 = 15.1 ft above the water, how far is the ship from the rocks?

Answer 1

well if d is horizontal, subtract that 17.4 at the end

the light is 47 - 15.1 = 31.9 ft above our horizontal line of sight

horizontal distance to light = 31.9 tan 29.3

d from rocks = that - 17.4

Answer 2

When I did that My answer came to be .501 but it was marked wrong. Was that the answer I was supposed to get?

Answer 3

I am sure that is wrong. You are not half a foot from the rocks.
whoops typo
31.9 / tan 29.3 upside down

Answer 4

31.9/tan 29.3 = 56.84
56.84 - 17.4 = 39.4

Answer 5

Okay this time my answer came to be 39.4 m but it still says incorrect. Did I not do my calculations correctly?

Answer 6

Do we have the picture right? Is subtracting 17.4 correct ?

Answer 7

yes

Answer 8

Then I am at a loss.

Answer 9

Hmmm. I get

(47.0-15.1)/(x-17.4) = tan 29.3 = 0.56
x = 74.36

Answer 10

As my final answer do I use ft or m ?

Answer 11

I put the lighthouse on the cliff, Steve put it out in the water. Which is it in your picture?

Answer 12

You whole problem is in feet, so I assume you would answer in feet unless your class has a rule saying always reply in SCI units.

Answer 13

Sorry you were right my unit was wrong, thanks!

Answer 14

I put the lighthouse so its peak was 47 ft above the water (as stated), regardless of the cliff.

Answer 15

I put the lighthouse behind the rocks. You put it ahead of the rocks. Could be either. (Boston Light versus Deer Island light)

Answer 16

Tan29.3 = (47-15.1)/(17.4+d2)
(17.4+d2)*Tan29.3 = 47-15.1 = 31.9
(17.4+d2) = (47-15.1)/Tan29.3 = 56.9
d2 = 56.9-17.4 = 39.5 Ft.