<PRE><B>Question 1122327</B>
this forms triangle SBU where angle SBU = 27 degrees and angle SUB = 65 degrees.


angle BSU is equal to 180 - 27 - 65 = 88 degrees.


88 + 27 + 65 = 180, as it should, since the sum of the interior angles of a triangle is 180 degrees.


BU = 16 kilometers.


use the law of sines to find the length of sides BS and SU.


law of sines says:   a/sin(A) = b/sin(B) = c/sin(C)


applied to this triangle, you get 16/sin(88) = SU/sin(27) = SB/sin(65)


this can be broken up into:


16/sin(88) = SU/sin(27) and 16/sin(88) = SB/sin(65)


cross multiply each to get:


16 * sin(27) = sin(88) * SU and 16 * sin(65) = SB * sin(88)


solve for SU to get SU = 16 * sin(27) / sin(88) = 7.298275633


solve for SB to get SB = 16 * sin(65) / sin(88) = 14.50976355


the distance from S to the nearer lighthouse is 7.298275633 kilometers.








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