Using the law of sines, the distance between tower B and the fire is: 7 miles.
What is the Law of Sines?
Law of Sines is given as:
sin A/a = sin B/b = sin C/c
Let the position of the fire be represented as C.
Thus:
m∠C = 180 - 42 - 64 = 74°
c = 10 miles
m∠A = 42°
Distance between tower B and the fire = a
Therefore:
sin 42/a = sin 74/10
a = (sin 42 × 10)/sin 74
a = 7 miles
Therefore, using the law of sines, the distance between tower B and the fire is: 7 miles.
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