How do I answer this navigation problem?

Find the width of a river that flows due east, if a surveyor finds that a tree on the opposite bank has a bearing of N2230'E from a certain point and a bearing of N15W from a point 400 feet downstream.

1 Answer
Alan P.
Mar 21, 2018

#color(blue)(188.887)# feet (approximately)

Explanation:

Here is what the situation looks like:
enter image source here

We have
#color(white)("XXXXXX")a+b=400color(white)("xx")rarrcolor(white)("xx")b=400-a#
and
#color(white)("XXX")w=a * sin(67^circ30')=b * sin(75^circ)#
#color(white)("XXXXXXXXXXXXXXX")=(400-a) * sin(75^circ)#

#rArrcolor(white)("XXX")a=(400 * sin(75^circ))/(sin(67^circ30')+sin(75^circ))#

with the aid of a calculator (and remembering that #67^circ30' = 67.5^circ#)

we can determine that
#color(white)("XXX")a=204.4498015187# feet (approx.)
and
#color(white)("XXX")w=a * sin(67^circ30')=188.8869870491# feet (approx.)

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