Answer:
The distance between tower B and the fire is [tex]\approx 9.4 \,\,miles[/tex] which agrees with the third option listed among the list of possible answers.
Step-by-step explanation:
In order to understand which are our known elements of the triangle, we represent the quantities given in the diagram (please see attached image).
We understand that we can solve for the third angle in the triangle (the one defined by the vertex where the fire is by using:
[tex]180^o-64^o-42^o=74^o[/tex]
Now that we know all angles, we can use a proportion from the law of sines to find side "x" which is the distance between the fire and tower B:
[tex]\frac{10\,mi}{sin(74^o)} =\frac{x}{sin(64^o)} \\\frac{10\,mi\,*\,sin(64^o)}{sin(74^o)} =x\\x\approx 9.4 \,\,miles[/tex]
