To estimate the size of a lake, Leah starts at one end of the lake and walks 90 meters. Then, she turns 100 degrees and walks another 84 meters to the end of the lake. Please draw a diagram of this situation. Also, how long is the lake?

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Answer 1 · 2017-12-23T04:22:17

Length of the lake is #=111.94# meters.

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Leah starts at point #A#, walks #90# meters and reaches point #B#, then turns #100^@# and walks another #84# meters to reach the end of the lake.

#AB=c=90# meters

#BC=a=84# meters

#AC=b=# the length of the lake.

#/_ABC=80^@#. We will call this angle #/_B# for simplicity.

From the law of cosines, we have:

#b^2=a^2+c^2-2ac*cosB#

#b^2=84^2+90^2-2(84)(90)cos80^@#

#b^2=7056+8100-15120(0.1736)#

#b^2=15156-2624.83#

#b^2=12531.17#

Length of the lake is #=b=111.94# meters