A six-foot person walks from the base of a streetlight directly toward the tip of the shadow cast by the streetlight... (more down below)

Question

When the person is 12 feet from the streetlight and 5 feet from the tip of the streetlight's shadow, the person's shadow starts to appear beyond the streetlight's shadow.

(a) Draw a right triangle that gives a visual representation of the problem. Show the known quantities and use a variable to indicate the height of the streetlight.

(b) Use a trigonometric function to write an equation involving the unknown quantity.

h =

(c) What is the height of the streetlight?

______ ft

Answer 1

(a) I think the bottom left diagram reflects the problem.

First find theta. Theta is tan 6/5. tan^-1 6/5 = 50.2 deg.

(b) tan 50.2 = h/17

1.20 = h/17

h= 1.20* 17

(c) 20.4 ft.