Question

The lighthouse is 137.75 feet. Tammy is 5 feet tall. Her shadow is 1.8 feet long. What is the height of the lighthouse in terms of Tammy's height?

1) 27.55
2) 27.55 feet
3) 27.55 feet tall
4) 27.55 ft

Answer 1

The lighthouse is 27.55 times taller than Tammy. By setting up a proportion using the ratio of Tammy's height to her shadow length and the lighthouse's height, we calculate the height of the lighthouse in terms of Tammy's height.

Step-by-step explanation:

To determine the height of the lighthouse in terms of Tammy's height, we can set up a proportion based on the similar triangles created by Tammy and her shadow, and the lighthouse and its hypothetical shadow. Using the ratios of their respective heights to their shadow lengths, we can solve for the lighthouse's height in terms of Tammy's height.

Let L represent the lighthouse's height in terms of Tammy's height. We have:

Height of Tammy / Length of Tammy's shadow = Height of Lighthouse / L

5 feet / 1.8 feet = 137.75 feet / L

Now we cross multiply:

5L = 137.75 * 1.8

L = (137.75 * 1.8) / 5

L = 27.55

The lighthouse is 27.55 times taller than Tammy. So the correct answer is 1) 27.55.