In the triangle DEF, the angle F has the largest measure.
Law of Cosines
This law is represented by the equation: C²=A²+B²-2ABcos θ, where: A,B and C are the sides of a triangle and θ = angle.
For solving this question, you should apply the Law of Cosines, where:
DF=6, DE=11 and EF=7.
- Finding Angle D from Law of Cosines
7²=6²+11²-2*6*11*cos D
49=36+121-132*cos D
132*cos D=157-49
132*cos D=108
cos D= 108/132=9/11
arc cos (9/11)=35.1°
Then, D=35.1°
- Finding Angle F from Law of Cosines
11²=6²+7² -2*6*7*cos (F)
121=36+49-84*cos (F)
84 * cos (F)=-121+85
84* cos (F)=-36
cos (F)= -36/84=-3/7
arccos (-3/7)=115.4°
Then, F=115.4°
Like the sum of the internal angles of a triangle is 180°. You can find the angle E:
D+F+E=180°
35.1+115.4+E=180
150.5+E=180
E=180-150.5=29.5°
Read more about the Law of Cosines here:
brainly.com/question/8288607
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