# Triangle tangent to circle problem using derivatives

1. Oct 12, 2011

### oates151

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

A metal bar of length l in the ﬁgure below has one end attached at a point P to a circle ofradius a < l. Point Q at the other end can slide back and forth along the x–axis.

(a) Find x as a function of θ (θ=angle POQ).
(b) Assume the lengths are in centimeters and the angular speed,dθ/dt, is 2 radians persecond counter clockwise. Find the speed at which point Q is moving when θ =π/2 and when θ =π/4. Give units.

2. Relevant equations

3. The attempt at a solution

Having a hard time understanding what to do for this problem.

2. Oct 12, 2011

### Dick

'l' is fixed and 'a' is fixed. theta is variable. If theta=0 then x=l+a, if theta=(-pi) then x=l-a, right? You want to express x as function of theta. Use some trig, like the law of cosines.

3. Oct 12, 2011

### SammyS

Staff Emeritus
Can you find x in terms of , a, and θ .

Use the law of cosines.