Thread: Help with calculating distance using tan, sin and cos please?

Hi, I am having problems with this question! I would be so grateful for some help!!

Question: The ship's captain located a light at an angle of elevation of 35º. The light rests atop a 40-foot lighthous. Find the distance from the ship to the shore using the values provided below.

values:
sin 35º=0.574 sin 55º=0.819
cos 35º=0.819 cos 55º=0.574
tan 35º=0.700 tan 55º=1.428

Thank you very very much!

Originally Posted by Polkadotprincess19

Hi, I am having problems with this question! I would be so grateful for some help!!

Question: The ship's captain located a light at an angle of elevation of 35º. The light rests atop a 40-foot lighthous. Find the distance from the ship to the shore using the values provided below.

values:
sin 35º=0.574 sin 55º=0.819
cos 35º=0.819 cos 55º=0.574
tan 35º=0.700 tan 55º=1.428

Thank you very very much!

Hi Polkadotprincess19,

Draw yourself a nice picture.

Notice the lighthouse is opposite the 35 degree angle.

You're looking for the side adjacent to the 35 degree angle.

Any ideas?

This problem is very easy. The figure is a right triangle composed by the corners:
1) the ship
2) the top of lighthouse
3) the shore.
The calcul are made in photos that I attached.

lighthouse problem.bmp

It seems to me that you are assuming that the lighthouse is on the shore.
Many lighthouses are located off shore.
All that you can do I think is to calculate the distance to the lighthouse.

Yes, that's true. And to find out what's the distance to the land, in naval books it's specificated the placement of lighthouses relative to shore.

Yes, and that only helps if the lighthouse is on a direct line, otherwise it's a dogleg to the beach !

let the distance between ship and shore is 'x' and the distance between captain and the light house is 'y'(at an elevation 35º.

sin = opposite/hypotenuse
cos = adjacent/hypotenuse
so
sin 35º = 40/y
0.574 = 40/y
y = 40/0.574
y= 40000/574
y=69.6

cos 35 = x/y
0.819 = x/69.6
x=0.819 * 69.6
x= 57

So the distance from the ship to the shore is 57

What is the height of the captains eye?