# Derivative Word Problem - Trig Needed?

1. Jan 2, 2012

### Char. Limit

1. The problem statement, all variables and given/known data
Now this is a problem that my sister had on her Calculus homework, and I can't seem to figure it out. I believe a similar triangles argument is necessary, but I'm not sure, and trig always was my weak spot. The problem is as follows:

2. Relevant equations

3. The attempt at a solution

Well, we drew a nice triangle like so:

We know that dx/dt = 4/9 and that dX/dt (the x-axis on the larger triangle) is constant. But I can't seem to complete the problem...

2. Jan 2, 2012

### Dick

It isn't true that dX/dt is constant. It's getting longer too. What is true is that the ratio of the height and the length of the smaller and larger triangles are equal. Those are the similar triangles. Write that expression down.

3. Jan 2, 2012

### Char. Limit

What, so like this?

$$\frac{8}{x+X} = \frac{2}{x}$$

And then use dx/dt=4/9 to get an expression for X in terms of t?

4. Jan 2, 2012

### Dick

Solve that equation for X then differentiate both sides to get an expression for dX/dt in terms of dx/dt.

5. Jan 2, 2012

### Char. Limit

Thanks! I can't believe I missed that.