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.
Any bug, improvement, feedback then
