Consider triangle DEF , where d = 17 , e = 19 and f = 30 Determine the measure of the largest angle.

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03-11-2022
Mathematics

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Consider triangle DEF , where d = 17 , e = 19 and f = 30 Determine the measure of the largest angle.

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NaythenL190284idn NaythenL190284idn · Answer 1 · 2022-11-03T18:15:24-04:00

The Solution.

Certainly, the largest angle is angle F ( since it is the angle directly opposite the longest side)

By cosine rule, we have

[tex]\cos F=\frac{d^2+e^2-f^2}{2de}[/tex][tex]S\text{ubstituting 17 for d, 19 for e, and 30 for }f,\text{ we get}[/tex][tex]\cos F=\frac{17^2+19^2-30^2}{2\times17\times19}[/tex][tex]\begin{gathered} \cos F=\frac{289+361-900}{34\times19} \\ \\ \cos F=\frac{650-900}{646} \end{gathered}[/tex][tex]\cos F=\frac{-250}{646}=-0.3870[/tex]

Taking the cosine inverse of both sides, we get

[tex]F=\cos ^{-1}(-0.3870)=112.77^o[/tex]

Therefore, the correct answer is 112.77 degrees.

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