Answer to Question #15060 in Trigonometry for Divina Daguplo

Question

A shore station at point A is 5280 ft. from another at point B.Find the distance from each of the shore stations to an enemy ship at point C if angle ABC is 83°37' and angle BAC is 85°1'.

Answer 1

Let's use the law of sines:

BC/sin(BAC) = AC/sin(ABC) = AB/sin(ACB)

BC/sin(85°1') = AC/sin(83°37') = 5280/sin(180-85°1'-83°37')

BC/sin(85°1') = AC/sin(83°37') = 5280/sin(11°22')

BC = 5280*sin(85°1')/sin(11°22') ≈ 23431.2 [ft].

AC = 5280*sin(83°37')/sin(11°22') ≈ 2240107.1 [ft].