Two boats start their journey from the same point A and travel along directions AC and AD, as shown below:

ABC is a right triangle with measure of angle ABC equal to 90 degrees and length of AB equal to 100 feet. There is a point C on BD such that measure of angle ACB is 60 degrees and measure of angle ADC is 30 degrees.

What is the distance, CD, between the boats?


Tan (60°)= 100 ft / BC ==> BC = 100 ft / tan(60°) tan (30°) = 100 ft / [BC + CD] ==> [BC + CD] = 100 ft / tan(30°) CD = 100 ft (1/tan(30°) - 1/ tan(60°)) = 115.47 ft

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