Answer:
(A)The northern lighthouse is 8.2 miles closer than the southern lighthouse.
Step-by-step explanation:
The triangle attached represents the given problem.
First, let us determine the distance of the Boat from each of the lighthouse.
In Triangle ABC,
∠A+∠B+∠C=180 degrees
21+∠B+16=180
∠B=180-37=143 degrees.
Using Law of Sines
[tex]\frac{a}{Sin A}=\frac{b}{Sin B}\\\frac{a}{Sin 21^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\a*sin143=60*sin21\\a=60*sin21\div sin143\\a=35.73 miles[/tex]
Similarly
[tex]\frac{c}{Sin C}=\frac{b}{Sin B}\\\frac{c}{Sin 16^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\c*sin143=60*sin16\\c=60*sin16\div sin143\\c=27.48 miles[/tex]
Difference in Distance =35.73-27.48=8.25 miles
Therefore, the northern lighthouse is 8.2 miles closer than the southern lighthouse.
