I am suppose to work this out somehow but I am not sure. I have tried many ways and I can't progress any further.
A streethg light his mounted at the top of a 15 ft tall pole. A man 6 ft tall walks away from the pole at a speed of 5ft/s along a straight path. How fast is the tip of the shadow moving when he is 40tf from the pole?
From this I know that I have a triangle with 2 known values on it, 15tf tall and then an opposite side of that is 6 feet tall. The rate of change of the bottom of the triangle is 5. I need to solve for c prime I am pretty sure. I am just not sure how to get that. I tried many different ways and none are correct.I tried to set up the pythagorean theorem but it didn't work and I am not sure why. I know that if I have 2 sides of a triangle I can figure out a third, so I tried to find the derivative of that but that didn't work.
Best Answer
The $15$ foot tall lightpole and the $6$ foot tall man aren’t sides of the same triangle. You actually have two triangles. Let $A$ be the point at the base of the lightpole, $B$ the point at the top of the lightpole, $C$ the point where the man is standing, $D$ the top of his head, and $E$ the end of his shadow. Then you have a right triangle $ABE$ with a vertical side of $15$ feet and another right triangle $CDE$ with a vertical side of $6$ feet. These triangles are related in a rather special way: they’re _______?
Now let $x$ be the distance of the man from the lightpole, i.e., the length of $\overline{AC}$. You know what $dx/dt$ is. Let $y$ be the length of $\overline{AE}$, the distance from the lightpole to the tip of his shadow. You want to find $dy/dt$. If you can answer the question above, you should be able to find a relationship between $x$ and $y$ that you can use to find $dy/dt$.