SOLUTION: A pier 1250 meters long extends at an angle from the shoreline. A surveyor walks to a point 1500 meters down the shoreline from the pier and measures the angle formed by the ends

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Question 1114609: A pier 1250 meters long extends at an angle from the shoreline. A surveyor walks to a point 1500 meters down the shoreline from the pier and measures the angle formed by the ends of the pier. if is found to be 53 degrees. What acute angle (correct to the nearest 0.1 degrees) does the pier form with the shoreline? is there more than one possibility? if so, how can we know which is the correct one?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A pier 1250 meters long extends at an angle from the shoreline.
A surveyor walks to a point 1500 meters down the shoreline from the pier and measures the angle formed by the ends of the pier.
if is found to be 53 degrees.
What acute angle (correct to the nearest 0.1 degrees) does the pier form with the shoreline?
:
Draw this out, the pier leans toward the observer, Angle A is opposite 1500m
the 53 angle is opposite the length of the pier, 1250 m
Use the law of sines, we have
1500%2Fsin%28A%29 = 1250%2Fsin%2853%29
Cross multiply
1250*sin(A) = sin(53)*1500
do the math
sin(A) = 1197.95%2F1250
A = 73.41 degrees
Find the 3rd angle which is the angle formed by the pier and the shoreline
180 - 53 - 73.41 = 53.6 degrees
:
is there more than one possibility? if so, how can we know which is the correct one?
there are two possibilities but only one if it is an acute angle (<90degrees)