Question

question 3 (multiple choice, 4 points) (25149-mc)
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?
294.3 ft
115.5 ft
230.9 ft
173.2 ft

Explanation:

Step1: Find length of BC

$\tan(40^\circ) = \frac{100}{BC} \implies BC = \frac{100}{\tan(40^\circ)} \approx \frac{100}{0.8391} \approx 119.18$ ft

Step2: Find length of BD

$\tan(20^\circ) = \frac{100}{BD} \implies BD = \frac{100}{\tan(20^\circ)} \approx \frac{100}{0.3640} \approx 274.75$ ft

Step3: Calculate CD = BD - BC

$CD = 274.75 - 119.18 = 155.57 \approx 155.5$ ft

Answer:

155.5 ft