An observer from the top of a lighthouse 370 feet above sea level sees two sailboats in the water. The angles of depression to t
he boats are 12 degrees and 10 degrees. How far apart are the boats, to the nearest foot?
1 answer:
Answer:the sailboats are 358 feet apart.
Step-by-step explanation:
The diagram of the triangle representing the situation is shown in the attached photo.
B represents the position of the lighthouse.
D represents the position of the first sailboat.
C represents the position of the second sailboat.
x represents the distance between the two sailboats
We would apply trigonometric ratio
Tan # = opposite/adjacent
For triangle ABD,
Tan 12 = 370/AD
AD = 370/Tan 12 = 370/0.2126 = 1740.357 feet
For triangle ABC,
Tan 10 = 370/AC
AD = 370/Tan 10 = 370/0.1763 = 2098.695 feet
x = AC - AD = 2098.695 - 1740.357 = 358 feet
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