Question

coast guard station able is located l = 220 miles due south of station baker. a ship at sea sends an sos call that is received by each station. the call to station able indicates that the ship is located n55°e, the call to station baker indicates that the ship is located s60°e. use this information to answer the questions below. (a) how far is each station from the ship? the distance from station able to the ship is miles. (do not round until the final answer. then round to two decimal places as needed.)

Explanation:

Step1: Find the angles of the triangle

The angle at Station Able is $55^{\circ}$, the angle at Station Baker is $60^{\circ}$, and the third - angle of the triangle formed by Station Able, Station Baker and the ship is $180^{\circ}-(55^{\circ}+60^{\circ}) = 65^{\circ}$. The distance between Station Able and Station Baker is $L = 220$ miles.

Step2: Use the Law of Sines

Let the distance from Station Able to the ship be $a$ and the distance from Station Baker to the ship be $b$. According to the Law of Sines, $\frac{a}{\sin60^{\circ}}=\frac{b}{\sin55^{\circ}}=\frac{220}{\sin65^{\circ}}$.

Step3: Calculate the distance from Station Able to the ship

We know that $\frac{a}{\sin60^{\circ}}=\frac{220}{\sin65^{\circ}}$. Then $a=\frac{220\sin60^{\circ}}{\sin65^{\circ}}$.
$a=\frac{220\times\frac{\sqrt{3}}{2}}{\sin65^{\circ}}\approx\frac{220\times0.866025}{0.906308}\approx210.34$

Answer:

$210.34$