Answer:
a=11.8,b=12,c=8,A=68.7°, B=72°, C= 39.3°
Explanation:
Given data:
b = 12
c= 8
a= ?
∠B= 72°
∠C= ?
∠A=?
To find the missing angle we will use law of sine:
a/sinA=b/sinB=c/sinC
Find m∠C.
b/sinB = c/sinC
Substitute the values:
12/sin72°=8/sinC
Apply cross multiplication.
12*sinC=sin72° * 8
sinC=0.951*8/12
sinC=7.608/12
sinC= 0.634
C= 39.3°
Now we know that the sum of angles = 180°
So,
m∠A+m∠B+m∠C=180°
m∠A+72°+39.3°=180°
m∠A=180°-72°-39.3°
m∠A= 68.7°
Now find the side a:
a/sinA=b/sinB
a/sin68.7°=12/sin72°
Apply cross multiplication:
a*sin72°=12*sin68.7°
a*0.951=12*0.931
a=0.931*12/0.951
a=11.172/0.951
a=11.75
a=11.8 ....