The captain of a ship at sea sights a lighthouse which is 300 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 20 degrees. How far is the ship from the base of the lighthouse?

Question

anonymous · Answer

First, draw the picture, set up a triangle, and find that$$\cot 20^o = \frac{x}{300} \implies x=300 \cot 20^o $$After that, you just plug it into a calculator to get the answer, or use a trig table in a book if you are a true dinosaur like me.

anonymous · Answer

What do you mean by cot?

anonymous · Answer

By the way, this solution assumes the ship captain measures his angle from the surface of the water; it's a small detail, but we have no way to really assume anything else.

anonymous · Answer

Cotangent.  Are you not studying trig?

anonymous · Answer

I am but I have never heard of contangent

anonymous · Answer

It's the reciprocal of tangent.

anonymous · Answer

Tangent is opposite divided by adjacent; cotangent is adjacent divided by opposite.

anonymous · Answer

You would probably not use cotangent but let us set up the picture to see|dw:1400648167141:dw|

anonymous · Answer

Could I use the inverse of tangent and plug it into my calculator

anonymous · Answer

We can tell from the picture that we have the opposite side of the angle of elevation and the adjacent side is what we are trying to find. Since we know a relationship for Opposite and Adjacent sides we can use:$$Tan \theta = Opposite/ Adjacent$$

anonymous · Answer

So since you know the relationship and have all variables except for 1 you can solve the equation for the missing variable. Do not forget to set your calculator to degrees if it is not already.

anonymous · Answer

Thank you so much I forgot to set my calculator to degrees

anonymous · Answer

My pleasure, I hope that helps!

anonymous · Answer

Not tan inverse.  That gives the angle from the tan measurement.  If you want to set this up using tan instead of cot, it will look like$$\tan 20^o= \frac{300}{x} \implies x=\frac{300}{\tan 20^o}$$After you figure it all out, the answers will be the same.

anonymous · Answer

Have you got this now?

anonymous · Answer

Yes thank you so much

anonymous · Answer

No sweat.  Do math every day.