The height of an amusement park ride is 157.5 feet. If the ride's shadow is 60 feet long, how long will a person's shadow be if the person is 5.3 feet tall?
Question
The height of an amusement park ride is 157.5 feet. If the ride's shadow is 60 feet long, how long will a person's shadow be if the person is 5.3 feet tall?
Solution
To solve this problem, we can use the concept of similar triangles. The height of the ride and its shadow form one triangle, and the height of the person and their shadow form a smaller, similar triangle.
Step 1: Identify the known values. The height of the ride (Hr) is 157.5 feet, the shadow of the ride (Sr) is 60 feet, and the height of the person (Hp) is 5.3 feet. We want to find the shadow of the person (Sp).
Step 2: Set up a proportion. The ratio of the height of the ride to its shadow is equal to the ratio of the height of the person to their shadow. This can be written as:
Hr/Sr = Hp/Sp
Step 3: Substitute the known values into the equation. 157.5/60 = 5.3/Sp
Step 4: Solve for Sp. Cross-multiply to get: 157.5 * Sp = 5.3 * 60
Then divide both sides by 157.5 to solve for Sp: Sp = (5.3 * 60) / 157.5
Step 5: Calculate the value. Sp = 2.02 feet
So, a person who is 5.3 feet tall will cast a shadow approximately 2.02 feet long when the ride's shadow is 60 feet long.
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