Final answer:
To find the height of the lighthouse, we can use similar triangles and set up a proportion. Plugging in the given values and solving for the height of the lighthouse, we find that it is 2 times the length from point D to point A.
Explanation:
To find the height of the lighthouse, we can use the concept of similar triangles. Let's consider the triangles formed by the lighthouse, its shadow, the pole, and its shadow. Since the two triangles are similar, their corresponding sides are proportional. Therefore, we can set up the following proportion:
(Height of Lighthouse)/(Length of Lighthouse Shadow) = (Height of Pole)/(Length of Pole Shadow)
Plugging in the given values, we have:
(Height of Lighthouse)/(D to A) = 8 m/(D to A)
Cross multiplying, we get:
Height of Lighthouse = 8 m x (D to A)/(Length of Lighthouse Shadow)
Substituting the given length of the lighthouse shadow, which is 12 m, we find that the height of the lighthouse is 8 m x (D to A)/12 m = 2(D to A).
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