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Jackson wants to find the height of the statue at the center of the town's square. He measures the statue's shadow, and his friend's

shadow. His friend is 5.6 feet tall, and his shadow is 1.4 feet long. The statue's shadow is 2.2 feet long.

The height of the statue is ____feet. Since Jackson's height is 5.8 feet, his shadow will be____ feet.
a. 7.84
b. 22.4
c. 8.8
d. 6.6

User Shneur
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1 Answer

2 votes

Final answer:

Using a proportional relationship, the height of the statue is calculated to be 8.8 feet based on the provided measurements. The correct answer is option c.

Step-by-step explanation:

To find the height of the statue, we can use a proportion based on similar triangles. The ratio between the height of Jackson's friend and the length of his shadow will be the same as the ratio between the height of the statue and the length of its shadow. We set up the proportion as follows:

Friend's height / Friend's shadow length = Statue's height / Statue's shadow length

Plugging in the numbers, we have:

5.6 feet / 1.4 feet = Statue's height / 2.2 feet

Now, we solve for the statue's height:

Statue's height = (5.6 feet / 1.4 feet) × 2.2 feet

Statue's height = 4 × 2.2 feet

Statue's height = 8.8 feet

To find Jackson's shadow length, we use the same proportion:

Friend's height / Friend's shadow length = Jackson's height / Jackson's shadow length

5.6 feet / 1.4 feet = 5.8 feet / Jackson's shadow length

Now, we solve for Jackson's shadow length:

Jackson's shadow length = (5.8 feet × 1.4 feet) / 5.6 feet

Jackson's shadow length = 1.47 feet (rounded to two decimal places)

The correct option for the height of the statue is (c) 8.8 feet, and Jackson's shadow will be approximately 1.47 feet.

User TMan
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