Thread: 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.

Please help!

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.

Please help!

by Pythagorean theorem

derive it



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

Thank you! That makes sense.