Question

Can you please help me!!! A ship is sailing parallel with a straight coastline, but the captain doesn’t know how far from the shore his is. A lighthouse is visible to the ship, and the angle between the line of the ship and the lighthouse is 30◦. After traveling 3 miles, the captain measures the angle to be 75◦. How far does he determine the boat to be from the coastline [decimal preferred]? (This is not the distance from the boat to the lighthouse.)

Answer 1

I tried this problem but I'm not sure if it is correct or not, its just my jab at it? Do you happen to have the solutions available? I got a distance of about 2 miles. I can upload some diagrams once I draw them up.

Answer 2

Unfortunatly, I don't have the solutions available at this time. But, I would like to see your diagrams when they are ready....

Answer 3

All right, I'm cranking them out as we speak =)

Answer 4

Awesome! :)

Answer 5

tan 30 = y/x
tan 75 = y/ ( x -3)
=> √3 x/3 = √ 3 + 2 ( x -3)

Answer 6

x is the distance at 30 degree!
-> x -3 is the distance at 75 degree.

Answer 7

But if the ship is sailing parallel with the coastline, wouldn't the distance from the shoreline remain constant?

Answer 8

That's what I thought too....

Answer 9

From my pic match up with pic you post, that how I come up with the solution.

Answer 10

My x is y in the pic, ( somehow my vision just can see my way)
From x => y which is the parallel distance ( x in the your pic)

Answer 11

Yes, the distance y ( = x in your pic) is constant!

Answer 12

Ok, we just set just assigned different variables to the sides.

Answer 13

Solve from this system equa:
tan 30 = y/x
tan 75 = y/ ( x -3)

Answer 14

So that's the answer then?

Answer 15

All you do is solve it to get y is the parallel distance!

Answer 16

Solve the above equation, right?

Answer 17

Yes, tan 30 = √3/3, tan 75 = 3.732

Answer 18

Ok! :)
Thanks guys so much for helping me out!!!