Can someone help me solve for this angle?

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Answer 1 · 2018-03-01T01:17:41

#R=cos^-1(-4/14)#

The first answer is correct.

We'll have to use the Law of Cosines here, which states that

#a^2=b^2-c^2+(2bc)cos(A)#

In our case, #A=R,# so #a,# the side opposite to the angle whose cosine we want, is #4.5#

#b# and #c,# the other two sides, are #3.5# and #2#

#4.5^2=2^2+3.5^2-2(2)(3.5)cos(R)#

#20.25=4+12.25-14cos(R)#

#20.25=16.25-14cos(R)#

#4=-14cos(R)#

#cos(R)=(-4/14)#

Recall that if we have #cos(theta)=x, theta=cos^-1(x)#

Therefore,

#R=cos^-1(-4/14)#

The first answer is correct.