Related Rates I - Ladder against a wall

Ahh, related rates. One of my favorites, and a classic Calc I topic. In this video I take you through the first related rates problem I ever saw as a student, concerning a ladder leaning up against a wall.
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[@tasnimulsarwar9189]

Just awesome.
Many thanks for making this.

[@Imnotpixel2]

I didnt understand the part that how u got 5 as h

[@RealMikeDobbs]

So that's just Pythagorean Theorem. The ladder is 13 ft long, we know the base is 12 feet from the wall, so h^2 + 12^2 = 13^2

[@Imnotpixel2]

@@RealMikeDobbs yeh...I get it now ...thx a lot bruh

[@RealMikeDobbs]

Happy to help 😄

[@cianmckeon5969]

Is there a way of working this out when dx/dt is unknown?

[@RealMikeDobbs]

Do you mean dh/dt? In this problem we were solving for dx/dt, so it was unknown. In, general, you can only ever solve for one variable in one equation. So, you would either need an additional piece of information, or be provided with additional information so you can set up a system of equations.

[@caominhnguyen906]

what's mean "dh"

[@RealMikeDobbs]

dh, in this case means a small change in h. dt refers to a small change in time. Thus the fraction, dh/dt, refers to the rate of change of h, with respect to time.