Question

two boats start their journey from the same point a and travel along directions ac and ad, as shown below. what is the distance, cd, between the boats? 200 ft 173.2 ft 115.5 ft 284.3 ft 230.9 ft

Explanation:

Step1: Find length of \(BC\)

In right - triangle \(ABC\), \(\tan60^{\circ}=\frac{AB}{BC}\). Given \(AB = 200\) ft. Since \(\tan60^{\circ}=\sqrt{3}\), then \(BC=\frac{AB}{\tan60^{\circ}}=\frac{200}{\sqrt{3}}\) ft.

Step2: Find length of \(BD\)

In right - triangle \(ABD\), \(\tan30^{\circ}=\frac{AB}{BD}\). Given \(AB = 200\) ft. Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\), then \(BD = 200\sqrt{3}\) ft.

Step3: Calculate \(CD\)

\(CD=BD - BC\). Substitute \(BD = 200\sqrt{3}\) and \(BC=\frac{200}{\sqrt{3}}\) into the formula:

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Answer:

\(230.9\) ft