Question

A 15 foot street lamp casts a 9 foot shadow. If the street lamp is near a 71 foot building, find the length of the shadow casted by the building

Answer 1

The shadow cast by a 71-foot building, using the similar triangles formed by a 15-foot street lamp and its 9-foot shadow, would be approximately 42.6 feet long.

Step-by-step explanation:

To solve the problem of the shadow cast by the building using the information given by the street lamp, we can use similar triangles. The ratio of the height of the street lamp to its shadow (15 ft to 9 ft) will be the same as the ratio of the height of the building to the length of its shadow. So, to find the length of the shadow cast by the 71-foot building, we set up the proportion:

15 ft (lamp height) / 9 ft (lamp shadow) = 71 ft (building height) / x ft (building shadow)

Cross multiply to solve for x:

15x = 71 × 9

x = (71 × 9) / 15

x = 42.6 ft

Therefore, the shadow cast by the 71-foot building would be approximately 42.6 feet long.