To determine the height of the building, use proportions based on the similar triangles concept, taking the ratio of the pole's height to its shadow length and setting it equal to the ratio of the building's height to the combined shadow and distance length. Solving the proportion, we find that the building is approximately 500 feet tall.
Step-by-step explanation:
The question involves using proportions to find the height of a building given the length of the shadow cast by a pole of known height. Since the shadows of the pole and the building coincide, we can assume that the triangles formed by the pole, its shadow, and the light source (presumably the Sun) are similar to those formed by the building, its shadow, and the light source.
To calculate the height of the building, we set up a proportion considering that the corresponding sides of similar triangles are in the same ratio:
The ratio of the height of the pole to its shadow's length (9 ft to 3.25 ft) should be the same as the ratio of the height of the building (which we need to find) to the combined length of the shadow of the pole and the distance between the pole and the building (3.25 ft + 177 ft).
Let the height of the building be H feet; then:
9 ft / 3.25 ft = H ft / (3.25 ft + 177 ft)
Now we solve for H:
H ft = (9 ft / 3.25 ft) * (3.25 ft + 177 ft)
H ft ≈ 9 ft * (180.25 ft / 3.25 ft)
H ft ≈ (9 * 180.25) / 3.25
H ≈ 499.5
The building is approximately 500 feet tall when rounded to the nearest foot.
The probable question is attached in the image.