Question

What is the measure of ∠E, rounded to the nearest degree? 28 36 54 80

Answer 1

Answer: choice B) 36 degrees

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Work Shown:

Use the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
(DF)^2 = (EF)^2 + (DE)^2 - 2*(EF)*(DE)*cos(E)
6^2 = 10^2 + 7^2 - 2*10*7*cos(E)
36 = 100 + 49 - 140*cos(E)
36 = 149 - 140*cos(E)
36 - 149  = -140*cos(E)
-113 = -140*cos(E)
cos(E) = -113/(-140)
cos(E) = 0.80714285714286
E = arccos(0.80714285714286) 
E = 36.1822872211523 <<--- see note below
E = 36 degrees

Note: arccos is the arccosine function, or the inverse cosine function. Make sure you are in degree mode