# Related rates finding the dA/dt.

1. Jul 5, 2011

### athamz

1. The problem statement, all variables and given/known data
The measure of one of the acute angles of a right triangle is decreasing at the rate 1/36 pi rad/sec. If the length of the hypotenuse is constant at 40cm, find how fast the area is changing when the measure of the acute angle is 1/6 pi.

2. Relevant equations

3. The attempt at a solution
I used the formula for the area of a triangle which is 1/2 base times the height, using trigonometry function, I substitute the value of base with 40costeta and the height is 40sinteta. How will I differentiated A = 40costeta*40sinteta? Will I use the product rule to differentiate? where will I include or put the rate given?

2. Jul 5, 2011

### lanedance

so you have
$$A(\theta) = 40 cos(\theta) sin(\theta)$$

differentiate both sides with respect to t, you will need to use both chain & product rules

3. Jul 5, 2011

### athamz

oh.. meaning

$$dA/dt = (cos^2 [/theta] - sin^2 [/theta]) d[/theta]/dt$$

Where will I get the value for cos[/theta] and sin[/theta] ?

4. Jul 5, 2011

### lanedance

well you're given theta

5. Jul 5, 2011

### athamz

oh.. thank you so much..
Is it alright if I will get a negative answer?

6. Jul 5, 2011

### Char. Limit

A note: This equation actually becomes very easy to differentiate if you recognize that $40 sin(\theta) cos(\theta) = 20 sin(2 \theta)$.

7. Jul 6, 2011

### lanedance

i haven't checked if it is the correct answer, but assuming you've done the maths correctly a negative answer is fine, it just means the area is decreasing

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