Question

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a boat is 200 feet from shore. the angle its line of sight makes with pier a relative to the shoreline is 35°. the angle its line of sight makes with pier b relative to the shoreline is 75°. how far is pier a from pier b rounded to the nearest foot?
pier a is from pier b.

Explanation:

Step1: Calculate distance from boat to shore projection to A

Let $x$ = distance from projection to A. $\tan(35^\circ)=\frac{200}{x} \Rightarrow x=\frac{200}{\tan(35^\circ)}$
$x\approx\frac{200}{0.7002}\approx285.6$ feet

Step2: Calculate distance from boat to shore projection to B

Let $y$ = distance from projection to B. $\tan(75^\circ)=\frac{200}{y} \Rightarrow y=\frac{200}{\tan(75^\circ)}$
$\tan(75^\circ)\approx3.732 \Rightarrow y\approx\frac{200}{3.732}\approx53.6$ feet

Step3: Find distance between A and B

Distance $AB = x + y \approx285.6 + 53.6 = 339.2$ feet

Step4: Round to nearest foot

$339.2 \approx339$

Answer:

339