Problema Solution
From two observation points A and B, a sinking ship is spotted at point C. Angle CAB is 28° and angle ABC is 60°. The distance between A and B is 4.12 miles. How far is the ship from point A to the nearest hundredth of a mile?
Answer provided by our tutors
Angle CAB is 28°
Angle ABC is 60°
Angle BCA is 180 - (28 + 60) = 180 - 88 = 92°
the distance between A and B is 4.12 miles and will denote it with c = 4.12 miles
the distance between B and C we will denote with a
the distance between A and C we will denote with b
we need to find b
we will use Law of Sines formula
b/(sin ABC) = c/(sin BCA)
b/(sin 60) = 4.12/(sin 92)
by solving we find
b = 3.57 miles
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the ship is 3.57 miles from the point A.