# Trig question in calculus book

1. Jun 12, 2009

### pooker

1. The problem statement, all variables and given/known data

A small boat is being pulled toward a dock that is 10 feet above the water. The rope is being pulled in at a rate of 1.5 feet per second. Find the rate at which the angle the rope makes wit hthe horizontal is changing when 20 feet of rope is out.

2. Relevant equations
None

3. The attempt at a solution

Sadly it has been awhile since I have done anything like this. This section in our book is on inverse trig functions, and this is the only homework question like this. I have never had trig, so finding the change of the angle I assume it is asking in radians is something I do not know how to solve.

if the dock is ten feet above the water, 20 feet of rope is out, that makes this a 1,2 , sqrt(3) triangle. It means it already has a degree of 30, but this is about as far as I know how too work.

2. Jun 12, 2009

### HallsofIvy

But to get "rate of change", you need the general formula for the distance. Let the amount of rope out be h and the angle the rope makes with the horizontal $\theta$. You have a right triangle "opposite side" of length 10, hypotenuse of length h, and angle $\theta$. Which trig function gives you an equation out of that?

Once you get equation itself, you can convert to a "rate" equation by differentiating both sides.