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?

284.3 ft

115.5 ft

230.9 ft

173.2 ft

Answer 1

A little bit knowledge of Trigonometry is required.
In triangle ABC,
tan 60 = AB/BC. Thus \[100/BC = \sqrt{3}\]
=> \[BC = 100/\sqrt{3}\]

Now in triangle ABD,
tan 30 = AB/BD
\[100/BD = 1/\sqrt{3}\]
=> \[BD = 100\sqrt{3}\]
Thus CD = BD - BC
=> CD = 100 ((3-1)/1.732)
=> CD = 115.5 ft is the required answer