# 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!

#### masters

MHF Helper
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!

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?

#### draganicimw

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.

View attachment lighthouse problem.bmp

#### BobP

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.

#### draganicimw

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.

#### BobP

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

#### kalwin

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
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

#### bjhopper

What is the height of the captains eye?