Question

Mei is standing next to a statue in the park. If Mei is 5 feet tall, her shadow is 3 feet long, and the statues shadow is 10 1/2 feet long, how tall is the statue.

Answer 1

Using the concept of similar triangles and the proportion of Mei's height to her shadow length, we find that the statue is 17.5 feet tall.

Step-by-step explanation:

To determine the height of the statue, we can use the concept of similar triangles. Mei and the statue create similar triangles with their respective shadows, because the angle of the sun would be the same for both, creating the same angle of inclination for their shadows. Since the triangles are similar, the ratio of Mei's height to her shadow length will be the same as the statue's height to its shadow length.

To find the height of the statue, we use the following proportion:
Mei's height / Mei's shadow length = Statue's height / Statue's shadow length

This can be written as:

5 feet / 3 feet = Statue's height / 10.5 feet.

Now, we solve for the statue's height:

Multiply both sides by 10.5 feet to get: 5 feet / 3 feet × 10.5 feet = Statue's height.

Simplify the equation: (5 feet × 10.5 feet) / 3 feet = Statue's height.

Calculate: (52.5 feet²) / 3 feet = 17.5 feet.

Therefore, the statue is 17.5 feet tall.

Answer 2

The problem presented above is an example in which we can use the concept of ratio and proportion. The ratio between the heights of Mei and the statue should be the same to the ratio of their shadows. Letting x be the height of the statue.
5 ft/ x ft = 3 ft / 10.5 ft
The value of x from the equation above is 17.5 ft.