Find Angle A using Side a=3, Side b=4, Side c=5 (Law of Cosines)
Solution:
We have `a=3,b=4,c=5`
The law of cosines states that
`a^2=b^2+c^2-2 b c * cos(A)`
`:. 2 b c * cos(A)=b^2+c^2-a^2`
`:. cos(A)=(b^2+c^2-a^2)/(2 b c)`
`:. A=cos^(-1)((b^2+c^2-a^2)/(2 b c))`
`:. A=cos^(-1)((4^2+5^2-3^2)/(2*4*5))`
`:. A=cos^(-1)((16+25-9)/(2*4*5))`
`:. A=cos^(-1)((32)/(2*4*5))`
`:. A=cos^(-1)(0.8)`
`:. A=36.8699`
Perimeter `P=a+b+c=3+4+5=12`
Area `=1/2 bc*sin(A)=1/2 *4*5*sin(36.8699)=1/2 *4*5*0.6=6`
This material is intended as a summary. Use your textbook for detail explanation.
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