Final answer:
To find the height of the lighthouse, a proportion based on similar triangles created by the shadows cast by the person and the lighthouse is used. However, the calculation based on the supplied data gives a height of 76.8 ft, not matching any of the answer choices, suggesting an error in the question or options.
Step-by-step explanation:
The student is asking how to find the height of the lighthouse using the proportions of the shadows and the known height of a person. As in the example provided - a person standing at 5.6 ft tall casts an 8.5 ft long shadow - we can set up a proportion since the sun's rays are parallel, creating similar triangles. The proportion is:
Person's Height / Person's Shadow = Lighthouse's Height / Lighthouse's Shadow
Substituting the given values:
5.6 ft / 8.5 ft = Lighthouse's Height / 116 ft
We then solve for Lighthouse's Height:
Lighthouse's Height = (5.6 ft / 8.5 ft) × 116 ft
This calculation gives us the height of the lighthouse. After solving, we find that the height is 76.8 ft, which is not one of the provided options, indicating a possible error in either the question or the options given.