If the angle you want is a, and the 3rd angle is b, then by the law of sines,
1250/sin53 = 1500/sinb
But, a+b+53=180, so b=127-a
sin(127-a) = 1500sin53/1250 = 0.9583
so, 127-a = 73.4
a = 53.6
I'll let you decide whether there is a second possibility.
I need help with this application.
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. It is found to be 53 degrees.
What acute angle ( correct to the nearest 0.1 degree) does the pier form with the shoreline? Is there more than one possibility? If so, how can we know which is the correct one?
1 answer