SOLUTION: Hello! I need help solving this please: A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set properly. From

Question 978217: Hello!
I need help solving this please:
A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set properly. From point A, the biologist walks downstream 100 feet and sights to point C (see figure). From this sighting, it is determined that θ = 59�. How wide is the river?
Please explain each step.
Thank you
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Use the Law of Sines
a/sin a = c/sin c
There is a right triangle with the downstream leg 100 feet and angle to C 59 degrees.
sin 59/C is width of river
sin 31/A is 100 feet.
This is a right triangle
sin 31/100=sin 59/x
0.5150/100=0.8572/width.
Cross-multiply
0.5150* width=85.72
width=85.72/0.5150 = 166.45 feet.
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