Question 1203428: 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 = 58�. How wide is the river?
Please explain each step.
Thank you
Found 4 solutions by MathLover1, Theo, ikleyn, math_tutor2020:
Answer by MathLover1(20850)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! B is 100 feet from point A.
C is assumed to be directly across the river.
ABC right triangle is assumed.
AB is 100 feet long on one side of the river.
BC is perpendicular to AB with point C on the other side of the right.\
angle CAB is 58 degrees.
tan(CAB) = opposite / adjacent = BC / AB = BC / 100
since CAB is 58 degrees, you get tan(58) = BC / 100
solve for BC to get BC = 100 * tan(58) = 62.48693519 feet.
that's the width of the river.
here's my diagram.
if it's not accurate, please send an accurate picture.
Answer by ikleyn(52810)  (Show Source):
You can put this solution on YOUR website! .
Answer by @Theo is incorrect.
Use the solution and the answer by @MathLover1. They are correct.
Notice that we have no a figure from the post,
so the figure was re-created blindly, by the method of guessing.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Assuming that the tutor @MathLover1 has the correct diagram, then,
tan(angle) = opposite/adjacent
tan(58) = w/100
w = 100*tan(58)
w = 160.033452904106
w = 160.03
The width of the river is roughly 160.03 feet.
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As a side note, tan(45) = 1.
Because tangent is an increasing function, this must mean tan(58) > 1 and 100*tan(58) > 100 without needing a calculator.
It's not entirely clear how the tutor @Theo got 100 * tan(58) = 62.48693519 which is not correct.
If I had to guess, Theo made this calculation
100 / tan(58) = 62.48693519
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