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 200 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?

230.9 ft
284.3 ft
115.5 ft
173.2 ft

Question

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 200 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?

230.9 ft
 284.3 ft
 115.5 ft
 173.2 ft

Jocelynn · Answer

what do u think?

BlossomBoy · Answer

A

mhanifa · Answer

|dw:1622369604274:dw|
This is the drawing based on the question.

mhanifa · Answer

CD = BD - BC
CD = AB cot D - AB cot C
CD = AB( cot D - cot C)
CD = 200(cot 30 deg - cot 60 deg)
CD =  230.94 ft