Answer:
Law of Sines
Solve for ∠A:
[tex]∠A = 90° - 42°[/tex]
[tex]∠A = 48°[/tex]
Solve for ∠B:
[tex]∠B = 90° + 15°[/tex]
[tex]∠B = 105°[/tex]
Solve for ∠C:
[tex]∠C= 180° - (48° + 105°)[/tex]
[tex]∠C = 180° - 153°[/tex]
[tex]∠C = 27°[/tex]
Formula:
[tex] \frac{c}{ \sin(C) } = \frac{b}{ \sin(B) } [/tex]
Solution:
[tex] \frac{110}{ \sin(27) } = \frac{b}{ \sin(105) } [/tex]
[tex]110 \sin(105) = b \sin(27) [/tex]
[tex]b = \frac{110 \sin(105) }{ \sin(27) } [/tex]
[tex]b = 234.04[/tex]
Final Answer:
The fire is 234.04 miles away from the western station.
