Find Angle A using Side a=3, Side b=4, Angle B=45 (Law of Sines)
Solution:
The law of sines states that
`a/sin(A)=b/sin(B)=c/sin(C)`
We have `a=3,b=4,B=45`
`:.a/sin(A)=b/sin(B)`
`:.sin(A)=(a*sin(B))/b`
`:.A=sin^(-1)((a*sin(B))/b)`
`:.A=sin^(-1)((3*sin(45))/4)`
`:.A=sin^(-1)((3*0.7071)/4)`
`:.A=sin^(-1)(0.5303)`
`:.A=32.0278`
`A+B+C=180`
`:.C=180-(A+B)`
`:.C=180-(32.0278+45)`
`:.C=180-77.0278`
`:.C=102.9722`
`c/sin(C)=b/sin(B)`
`:.c=(b*sin(C))/sin(B)`
`:.c=(4*sin(102.9722))/sin(45)`
`:.c=(4*0.9745)/(0.7071)`
`:.c=5.5125`
perimeter `P=a+b+c=3+4+5.5125=12.5125`
Area `=1/2 ab*sin(C)=1/2 *3*4*sin(102.9722)=1/2 *3*4*0.9745=5.8469`
This material is intended as a summary. Use your textbook for detail explanation.
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