Problema Solution
The figure shows a 1175-yard-long sand beach and an oil platform in the ocean. The angle made with the platform from one end of the beach is 83 degrees and from the other end is 76 degrees. Find the distance of the oil platform, to the nearest tenth of a yard, from each end of the beach.
Answer provided by our tutors
Lets denote with 'x' and 'y' the distances we need to find.
Using the Law of Sines we can write:
x/(sin 76) = 1175/(sin(180 - (83 + 76))
x/(sin 76) = 1175/(sin 21)
x = 3,181.4 yd
y/(sin 83) = 1175/(sin(180 - (83 + 76))
y/(sin 83) = 1175/(sin 21)
y = 3,254.3 yd
The platform is 3,181.4 yards far from one end of the beach and 3,254.3 yd far from the other.