Question

A person 6 ft tall is standing near a street light so that the ration of his height to the pole is 2/3.a.Find the length of the pole.b.If the person head is exactly 5 ft from the light bulb, how far is the person from the pole?c.How long is the shadow? d. give coordinates of points A, C, D, E, F with B (0,0)

Answer 1

The picture shows the details. (a) DE=(2/3)AC, so AC=(3/2)DE=3*6/2=9'.

(b) DE=FC=6'; AF=AC-FC=9-6=3'; DF^2=AB^2-AF^2 (Pythagoras)=25-9=16, so DF=4'.

(c) BE/(BE+4)=2/3 (similar triangles BDE and BAC); 3BE=2BE+8; BE=8' (shadow length).

(d) all points shown on the picture with coordinates.