Law of Cosines!

~Law of cosines is only used when law of sines doesn't work.

~The formula is (leg)^2=(adj leg)^2+(other adj leg)^2-2(adj leg)(other adj leg)cos(the angle in between)

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~Ex.1: In triangle ABC: A=25, B=60, a=6, & c=8.

Find: C & b-

180-60-25=95

C=95

b^2=6^2+8^2-2(8)(6)cos(60)

*First you square root everything

*Then you plug it into your calculator exactly the way it is.

b=7.211

~Ex.2: In triangle XYZ: Z=43, X=16, x=4, & y=21

Find: Y & z-

180-43-16=121

Y=121

z^2=4^2+21^2-2(4)(21)cos(43)

*First you take the square root of everything

*Then you plug it into your calculator exactly the way it is.

z=18.279

~Ex.3: In triangle DEF: F=80, d=10, & e=3

FInd: D, E, & f-

f^2=3^2+10^2-2(3)(10)cos(80)

*First you take the square root of everything.

*Then you plug it into your calculator exactly the way it is.

f=9.929

10^2=3^2+9.929^2-2(3)(9.929)cosD

*First subtract the squares to the other side

*Next divide each side by -2(3)(9.929)

*Then take the inverse and plug it into your calculator

D=cos^-1((10^2-3^2-9.929^2)/(-2*3*9.929))

D=82.685

180-80-82.685=17.315

E=17.315