Question

The eastern point lighthouse in gloucester, massachusetts was established in 1832 to help fishermen into the harbor. it is still used today by the coast guard. a fisherman along the shore wanted to know how tall it was. he is 6 ft. tall and he measures his shadow to be 1.7 ft. the lighthouse casts a shadow of 10.2 ft., approximately how tall is the eastern point lighthouse?

a. 17.9 feet
b. 36 feet
c. 61.2 feet
d. 104 feet
e. 112 feet

Answer 1

To find the height of the eastern point lighthouse, we can use the concept of similar triangles. The height of the lighthouse is proportional to the length of its shadow, just like the height of the fisherman is proportional to the length of his shadow. Plugging in the given values and solving, the height of the lighthouse is approximately 36 feet.

Step-by-step explanation:

To find the height of the eastern point lighthouse, we can use the concept of similar triangles. The height of the lighthouse is proportional to the length of its shadow, just like the height of the fisherman is proportional to the length of his shadow. We can set up a proportion:

height of lighthouse / length of lighthouse's shadow = height of fisherman / length of fisherman's shadow

Plugging in the values, we get:

height of lighthouse / 10.2 = 6 / 1.7

Cross-multiplying and solving for the height of the lighthouse, we find:

height of lighthouse = (6 / 1.7) * 10.2

height of lighthouse ≈ 36 feet

Answer 2

To find the height of the eastern point lighthouse, we can use the concept of similar triangles. The height of the lighthouse is proportional to the length of its shadow, just like the height of the fisherman is proportional to the length of his shadow. Plugging in the given values and solving, the height of the lighthouse is approximately 36 feet.

Step-by-step explanation:

To find the height of the eastern point lighthouse, we can use the concept of similar triangles. The height of the lighthouse is proportional to the length of its shadow, just like the height of the fisherman is proportional to the length of his shadow. We can set up a proportion:

height of lighthouse / length of lighthouse's shadow = height of fisherman / length of fisherman's shadow

Plugging in the values, we get:

height of lighthouse / 10.2 = 6 / 1.7

Cross-multiplying and solving for the height of the lighthouse, we find:

height of lighthouse = (6 / 1.7) * 10.2

height of lighthouse ≈ 36 feet