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?

1 Answer
Dec 23, 2017

Length of the lake is =111.94 meters.

Explanation:

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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