Final answer:
To find the height of the street sign, we use the properties of similar triangles formed by the shadows of the sign and a parking meter. The parking meter is 4 feet tall with a 5-foot shadow, so the street sign, with a 10-foot shadow, is 8 feet tall.
Step-by-step explanation:
To determine the height of the street sign, we can use the properties of similar triangles. The shadows cast by the street sign and the parking meter form triangles that are proportional, assuming the light source (such as the sun) is sufficiently far away that the rays are essentially parallel.
The parking meter is 4 feet tall and casts a 60-inch shadow. Since there are 12 inches in a foot, the parking meter's shadow is 5 feet long (60 inches / 12 inches per foot = 5 feet). This gives us a ratio of height to shadow length for the parking meter of 4 feet in height per 5 feet of shadow.
Using this ratio, we can find the height of the street sign. If the street sign's shadow is 10 feet, then we set up a proportion where 4 feet (the meter's height) is to 5 feet (the meter's shadow) as the street sign's height is 10 feet (the sign's shadow):
4/5 = x/10, where x is the height of the street sign.
Solving for x gives us x = (4/5) * 10 = 8. Therefore, the height of the street sign is 8 feet.