Question
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?
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?
Answers
Steve
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.
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.