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Yang
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Tyro
Asked: 2021-04-08T12:29:03+00:00 In: ,

Find the length of the third side on the triangular shaped lot.

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A lot is triangular in shape. Two of its sides are 500m and 700m. The angle between these two sides is 100 degrees. Find the length of the third side.

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  2. acedstud

    The length of the third side of the triangle can be found using the cosine rule. The closing rule states that for a triangle with sides labeled a, b, c and the angles opposite a, b, c labeled A, B, C, then b^2=a^2+c^2-2ac\cos{B}.

    Thus, from the attached triangle b^2=500^2+700^2-2(500)(700)\cos{100^o}=250000+490000-(-121553.7244)

    =740000+121553.7244=861553.7244

    Thus, b=\sqrt{861553.7244}\approx928 m

    Therefore, the length of the third side is about 928 m.

    Attachment

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