# Related Rates Problem

• Jan 17th 2011, 09:19 PM
onanyc
Related Rates Problem
Let ABC be a right triangle with fixed hypotenuse, c= 10 inches. If x (the angle at vertex A) is increasing at a rate of 4pi radians/min, find the rate at which a (the side opposite A) is increasing at the instant that x = pi/3 radians.

(Thinking)
• Jan 17th 2011, 09:58 PM
pickslides
Here's some hints

$\displaystyle \frac{dx}{dt} = 4\pi$

$\displaystyle\sin x = \frac{a}{10} \implies a = 10\sin x$ then $\displaystyle\frac{da}{dx} = 10\cos x$
• Jan 17th 2011, 10:06 PM
Prove It
And you want to evaluate $\displaystyle \frac{da}{dt} = \frac{dx}{dt}\,\frac{da}{dx}$ at the point where $\displaystyle x = \frac{\pi}{3}$.