Street light Calculus Problem

Question

A street light is at the top of a 20-ft-tall pole. A 6-ft tall woman walks away from the pole with a speed of 7 ft/sec along a straight path (see figure). How fast is the tip of her shadow moving, in ft/sec, when she is 35 ft from the base of the pole?

Answer 1

Let x be the distance the woman is from the pole and y the length of her shadow. Draw a right triangle with 20 as the height and x + y as the base. There is a smaller right triangle within this with 6 as the height (the woman) and y as the base (her shadow). Using similar triangles, y/6 = (x+y)/20. Solve for y to get y = (3/7)x. Then dy/dt = (3/7)dx/dt. Plug in dx/dt = 7 to get dy/dt. You don't need the 35 since dy/dt is constant.