Professor plum is standing 10 feet from a street lamp the light from the lamp is making his shadow 8 feet long. he estimates that the angle of elevation from the tip of his shadow to the top of the street lamp is 40 degrees. about how high is the street lamp?

It would be helpful to draw the figure from the problem statement above. Drawing it, would give you a right triangle shape where the base is equal to 10 ft + 8 ft = 18 ft with the angle of 40 degrees. We use knowledge on trigonometric functions to solve this.

tan (theta) = opposite side / adjacent side
tan 40 = x / 18
x = 15.10 ft