Question

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

Answer 1

The Solution.

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

By cosine rule, we have

`\cos F=(d^2+e^2-f^2)/(2de)`
`S\text{ubstituting 17 for d, 19 for e, and 30 for }f,\text{ we get}`
`\cos F=(17^2+19^2-30^2)/(2*17*19)`
`\begin{gathered} \cos F=(289+361-900)/(34*19) \\ \\ \cos F=(650-900)/(646) \end{gathered}`
`\cos F=(-250)/(646)=-0.3870`

Taking the cosine inverse of both sides, we get

`F=\cos ^(-1)(-0.3870)=112.77^o`

Therefore, the correct answer is 112.77 degrees.