In triangle DEF, given the lengths of the sides, find the measure of the stated angle to the nearest degree.

d = 5.4
e = 10.5
f = 10.8;
m

Question

In triangle DEF, given the lengths of the sides, find the measure of the stated angle to the nearest degree. 

d = 5.4 
e = 10.5 
f = 10.8; 
m<F

jim_thompson5910 · Answer

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jim_thompson5910 · Answer

use the law of cosines to find angle F

f^2 = d^2 + e^2 - 2*d*e*cos(F)

10.8^2 = 5.4^2 + 10.5^2 - 2*5.4*10.5*cos(F)

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...
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F = ??

warpedkitten · Answer

@jim_thompson5910 I keep using that, however I never get a straight answer. I use Mathway and it gives me 

116.64=139.41-113.4cos(F)

and then I'm not sure what to do with it.

jim_thompson5910 · Answer

Let z = cos(F) for now. If we replace cos(F) with z, we get this equation

10.8^2 = 5.4^2 + 10.5^2 - 2*5.4*10.5*z

are you able to solve for, or isolate, z?