An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far sides of an island to
be 16.5 and 10.5 respectively. How long is the island ?
1 answer:
Answer:
154.10 Feets
Step-by-step explanation:
Given the following :
Height (h) of cliff = 320 feet
Angle of depression of near side = 16.5°
Angle of depression of far side = 10.5°
Using trigonometry :
We can obtain x and y as shown in the attached picture :
Tanθ = opposite / Adjacent
Adjacent = height of cliff = 320 Feets
For the near side :
Tanθ = opposite / Adjacent
Tan (16.5°) = x / 320
0.2962134 = x / 320
x = 0.2962134 * 320
x = 94.788318 Feets
For the far side :
Tanθ = opposite / Adjacent
Tan (10.5°) = x / 320
0.1853390 = x / 320
x = 0.1853390 * 320
x = 59.308494 Feets
Length of island = (59.308494 + 94.788318) feet
= 154.10 Feets
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