A biologist wants to know the width of a river in order to properly set instruments for studying the pollutants in the water. From point A which is straight across the river from point C, the biologist walks downstream 70 feet to Point B and sights to point C. From this sighting, it is determined that θ = 54º. How wide is the river to the nearest foot?

Guest Oct 28, 2017

If you draw a picture of his path, it looks like this..



It makes a right triangle, and side AC is the width of the river. In every right triangle,


tan θ  =  opposite / adjacent


tan 54°  =  AC / 70                   Multiply both sides by  70 .


70 tan 54°  =  AC


96 feet  ≈  AC

hectictar  Oct 28, 2017

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