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Trigonometry - Sine Rule

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Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can be expressed as matrices. Help them solve the following problems.
A ranger in fire tower A spots a fire at a direction of 295 degrees. A ranger in fire tower B, located 45 miles at a direction of 45 degrees from tower A, spots the same fire at direction of 255 degrees. How far from tower A is the fire? From tower B?

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The expert examines research at the National Interagency Fire Center in Boise, Idaho. Neat and step-by-step solution with sketch is provided.

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We need to find: AF and BF.
In ABF, AB = 45 miles by ...

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