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 300 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?

Answer 1

*See the figure in the attachment below

Answer:

346.4 ft

Step-by-step Explanation:

The distance between the boats, CD = BD - BC

Using trigonometric ratio formula, find the length of BD in right triangle ∆ABD, and also find the length of BC in right triangle ABC.

Length of BD in triangle ABD:

Opposite length to <30° = 300 ft

Adjacent length = BD

$tan(30) = \frac{300}{BD}$

$BD*tan(30) = 300$

Divide both sides by tan(30)

$\frac{BD*tan(30)}{tan(30)} = \frac{300}{tan(30)}$

$BD = 519.6 ft$ (nearest tenth)

Length of BC in triangle ABC:

Opposite length to <60° = 300 ft

Adjacent length = BC

$tan(60) = \frac{300}{BC}$

$BC*tan(60) = 300$

Divide both sides by tan(60)

$\frac{BC*tan(60)}{tan(60)} = \frac{300}{tan(60)}$

$BC = 173.2 ft$ (nearest tenth)

distance between, CD, between the boats = BD - BC

= 519.6 - 173.2 = 346.4 ft

Answer 2

346.4 ft is the correct answer