# Homework Help: Cranks and Pistons

1. Feb 1, 2005

Hello all

I was given a problem involving cranks and pistons. I do not understand the exact question, but it involved an oblique triangle where you had to apply the Law of cosines. Lets say you are given $$\theta = \frac{\pi}{4}, x=7, c = 11$$ where $$c$$ where c is the hypotenuse and $$\frac{dx}{dt} = 200$$. Find the rate of change of the piston.

So here it is:

$$c^2 = a^2 + b^2 - 2ab\cos C$$
$$a^2 = b^2 + c^2 - 2bc\cos A$$
$$b^2 = a^2 + c^2 - 2ac\cos B$$

Ok so how would I solve for the change of the piston? Would I just find the derivative of the first Law of Cosine expression and substitute in the values?

2. Feb 1, 2005

### dextercioby

Okay,what's the connection betweent the 4 variables:a,b,c & x??

Daniel.

3. Feb 1, 2005

### HallsofIvy

What is x and what in the world is "the change of the piston"? (How does a piston change?)

4. Feb 1, 2005

sorry I meant to say the rate of change of the piston . $$x$$ is one of the sides of the triangle.

5. Feb 1, 2005

### dextercioby

Still doesn't make too much sense... :grumpy: What about a,b,c ???What are they...??

HINT:Post the initial problem's text in original form... :grumpy:

Daniel.