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 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? a284.3 ft b115.5 ft c230.9 ft d173.2 ft

Answer 1

Answer:

$B\text{ : 115.5 ft}$

Explanation:

Here, we want to get the distance between the boats

We can firstly calculate BC using triangle ABC

To do that, we use the appropriate trigonometric identity

We have the opposite and we want to calculate the adjacent

We can use the tan (this is the ratio of the opposite length to the adjacent length)

Thus:

$\begin{gathered} Tan\text{ 60 = }\frac{100}{BC} \\ \\ BC\text{ = }\frac{100}{Tan\text{ 60}}\text{ = 57.74 ft} \end{gathered}$

We can apply a similar principle to get BD in triangle ABD

$\begin{gathered} Tan\text{ 30 = }\frac{100}{BD} \\ \\ BD\text{ = 173.21 ft} \end{gathered}$

From the image:

$\begin{gathered} CD\text{ = BD - BC} \\ CD=\text{ 173.21 - 57.74} \\ CD\text{ = 115.5 ft} \end{gathered}$