Question

a person 69 inches tall stands 40 feet from the base of a streetlight. the street light casts a shadow of length 96 inches how far above the ground is the streetlight

Answer 1

See the attachment.
AO = height of street light = H
AB = distance of person from base of street light = 40 feet
AB = 40*12 inches = 576 inches
BC = shadow length = 96 inches

ΔOAC and ΔMBC are similar. So

$\frac{OA}{AC} = \frac{MB}{BC} \\ \\ \frac{H}{576+96} = \frac{69}{96} \\ \\\frac{H}{672} = \frac{69}{96} \\ \\H= \frac{69}{96} \times 672\\ \\ H=69 \times 7=\boxed{483\ inch}$

483 inch = 483/12 feet = 40 feet 3 inch
So the street light is 40 feet 3 inch above the ground.