# Trigonometry Word Problem involving Inverse trigonometric functions

1. Aug 31, 2012

### acen_gr

1. The problem statement, all variables and given/known data
A ship is d feet from a dock (horizontal distance). The dock is 40 feet above sea level. The angle of depression from the dock to the ship is θ. Write θ as a function of d.

2. Relevant equations
This question is accompanied with choices. The choices are
$$(A) θ = 40arctan(d)$$
$$(B) θ = arctan(\frac{40}{d})$$
$$(C) θ = arcsin(\frac{d}{60})$$
$$(D) θ = \frac{arctan(d)}{40}$$
$$(E) none of these$$

3. The attempt at a solution
First, I would like to know if my graphical representation of this problem is correct.

Thank you!

Last edited: Aug 31, 2012
2. Aug 31, 2012

### HallsofIvy

Staff Emeritus
Do you know the definitions of "sine", "tangent", etc.? If not, look them up. Once you know them you will see that this problem is trivial.

3. Aug 31, 2012

### ehild

It is a very nice (and correct) drawing, with a very big ship.

ehild

4. Aug 31, 2012

### acen_gr

Ok sir so if my interpretation of the problem is right, then it would be right if I answer choice B right? Thank you!

5. Aug 31, 2012

### ehild

YES!

ehild

6. Aug 31, 2012

### acen_gr

Yes! I made it right. I just wonder if my understanding was right because I'm not from an English-based country so some phrasing are not clear to me. Thank you everyone!