Answer: 94.72ft and 59.2ft
Step-by-step explanation:
Tan16.5=x/320
320tan16.5= 0.296
320(0.296)=94.72ft
Tan10.5=y/320
320tan10.5=0.185
320(0.185)=59.2ft
The length of the island to nearest foot is 2807 feet
From the question, we are to determine the length of the island
Consider the diagram,
/DB/ is the height of the cliff
The length of the island is /AC/
First, we will calculate /AB/
Consider ΔABD
Using SOH CAH TOA
[tex]tan 16.5^\circ = \frac{/DB/}{/AB/}[/tex]
[tex]tan 16.5^\circ = \frac{320}{/AB/}[/tex]
[tex]0.2962= \frac{320}{/AB/}[/tex]
[tex]/AB/=\frac{320}{0.2962}[/tex]
/AB/ = 1080.35 feet
Now, we will calculate /BC/
Consider ΔDBC
[tex]tan 10.5^\circ = \frac{/DB/}{/BC/}[/tex]
[tex]tan 10.5^\circ = \frac{320}{/BC/}[/tex]
[tex]0.1853= \frac{320}{/BC/}[/tex]
[tex]/BC/=\frac{320}{0.1853}[/tex]
/BC/ = 1726.93 feet
In the diagram,
/AC/ = /AB/ + /BC/
/AC/ = 1080.35 feet + 1726.93 feet
/AC/ = 2807.28 feet
/AC/ ≅ 2807 feet
Hence, the length of the island to nearest foot is 2807 feet.
Learn more on Trigonometry here: https://brainly.com/question/17022372
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