a man 6.2 feet tall stands 12 feet away from a streetlight and casts a 5 ft shadow.
How tall is the streetlight?
Draw a little sketch to convince yourself that the shadow of the light is 12'+ 5'=17'
Use proportions and cross product:
6.2 ft : 5 ft shadow
? ft : 17 ft shadow
height of light
= 6.2*17/5
= 21.08'
To find the height of the streetlight, we need to use similar triangles. Comparing the man's height, the length of his shadow, and the distance between the man and the streetlight, we can set up the following proportion:
(man's height) / (man's distance from the streetlight) = (streetlight's height) / (length of the shadow)
Let's solve for the height of the streetlight:
(man's height) = 6.2 feet
(man's distance from the streetlight) = 12 feet
(length of the shadow) = 5 feet
Substituting these values into the proportion:
6.2 / 12 = (streetlight's height) / 5
Cross multiplying, we get:
(6.2 * 5) = (12 * streetlight's height)
31 = 12 * streetlight's height
Dividing both sides by 12:
31 / 12 = streetlight's height
The height of the streetlight is approximately 2.58 feet.