Answer:
4.7 units
Step-by-step explanation:
We are given that in triangle ABC
AB= 3 units
Angle ABC=76 degree
Angle CAB=66 degrees
AC=b
We have to find the approximate value of b using sin laws.
We know that sum of angles of a triangle =180 degrees
[tex]\angle CAB+\angle ABC+\angle ACB=180[/tex]
[tex]76+66+\angle ACB=180[/tex]
[tex]142+\angle ACB=180[/tex]
[tex]\angle ACB=180-142=38^{\circ}[/tex]
We know that law of sines
[tex]\frac{BC}{Sin A}=\frac{AC}{SinB}=\frac{AB}{sin C}[/tex]
Substitute the values then we get
[tex]\frac{b}{sin 76^{\circ}}=\frac{3}{sin 38^{\circ}}[/tex]
[tex] b=\frac{3}{sin 38^{\circ}}\times sin 76^{\circ}[/tex]
[tex] b=4.7[/tex]
Hence, the value of b= 4.7 units
