# Thread: Triangle dz/dt question

1. ## Triangle dz/dt question

The sides of a right triangle are x, y, and z with z being the hypoteneuse. If the sides are increasing in such a way that dz/dt = 1, dx/dt = 3dy/dt, find dy/dt at the instant x = 12 and y = 5.

I know that z = 13 according to the Pythagorean Theorem, but beyond that I do not know what to do. I guess my problem is I do not understand how derivatives relate to the sides of a triangle. I've only used them with functions before.

2. Originally Posted by poitier
The sides of a right triangle are x, y, and z with z being the hypoteneuse. If the sides are increasing in such a way that dz/dt = 1, dx/dt = 3dy/dt, find dy/dt at the instant x = 12 and y = 5.

I know that z = 13 according to the Pythagorean Theorem, but beyond that I do not know what to do. I guess my problem is I do not understand how derivatives relate to the sides of a triangle. I've only used them with functions before.

by Pythagorean theorem

$\displaystyle z^2 = x^2 + y^2$ derive it

$\displaystyle 2 z \frac{dz}{dt} = 2 x \frac{dx}{dt} + 2 y \frac{dy}{dt}$

dz/dt , dx/dt , x ,y these things are given you find z =13 sub these to what I get to find dy/dt

3. Thank you! That makes sense.