Question

A 5 ft 3 person casts a shadow 3 feet long, a Rollercoaster casts a shadow 40 feet long at the same location and time of day. How tall is the Rollercoaster?

a) 20 ft
b) 25 ft
c) 30 ft
d) 35 ft

Answer 1

The height of the roller coaster can be calculated using similar triangles. The correct height calculation results in 14 feet 7 inches, which is not one of the provided multiple-choice options, indicating there may be an error in the question or the given answer choices.

Step-by-step explanation:

The height of the roller coaster can be determined using the concept of similar triangles. Here, the person and their shadow create one triangle, while the roller coaster and its shadow create a larger, similar triangle because the angles are the same. This is the basis for solving this type of proportion problem. If the person is 5 feet 3 inches (which is 63 inches) tall and their shadow is 3 feet (36 inches) long, we can set up a proportion with the roller coaster's shadow being 40 feet (480 inches) long.

The proportion would then be:

• Person's height / Person's shadow = Roller coaster's height / Roller coaster's shadow
• 63 inches / 36 inches = Roller coaster's height (in inches) / 480 inches

By cross-multiplying to solve for the roller coaster's height, we get:

• 
  (63 inches / 36 inches) * 480 inches = Roller coaster's height
  
• 
  175 inches = Roller coaster's height
  

Now, converting the roller coaster's height back into feet:

• 
  175 inches / 12 inches per foot = 14 feet 7 inches tall
  

Since this is not an option in the multiple-choice answers provided, it's likely there was an error in the question or one of the given answer choices. Sometimes there might be mistakes or typos in the question. If needed, clarification should be sought from the source of the question.