Andy C. answered • 04/06/18

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A triangle is formed by the paths taken by the ship.

1 knot = 1.15078 mph

Starting from the origin (0,0)

The first side of the triangle is

2 hours x 15 x 1.15078 mph = 34.5234 miles

at 40 degrees above the x-axis

From there, the ship turns 80 Southeast

and travels 3 x 20 x 1.15078 = 69.0468 miles.

So the second side is 69.0468 miles forming

an 80 degree angle.

IN summary, we have a triangle with sides

34.5234 and 69.0468

having angles 40 degrees and 80 degrees.

The third side is the measure we are trying to find.

It can be found using the Law of Sines formula, which

states the RATIOS of each side and the OPPOSITE angle

are proportional. SPECIFICALLY, a / sin A = b / sin B = c / sin C

So the missing side is X / sin 80 = 69.0468 / sin 40

X = 69.0468 / sin 40 * sin 80 = 105.78