Answer:
a) the angle ABC is approximately 106 degrees b) 24
Step-by-step explanation:
1) Using the law of cos
AC*AC= AB*AB+BC*BC-2*AB*BC*cosB
8*8= 5*5+5*5-2*5*5*cosB
64= 50- 50c0sB
cosB= 14/(-50)= -7/25.
B= arccosB= arccos(-7/25)= 106degrees.
2) sinB*sinB= 1- CosB*cosB= 1-49/625= 576/625
sinB= 24/25 (SinB doesn't equal -24/25, because B is between 0 and 180 degrress, so sin B is positive)
3) S= AB*BC*sinB= 5*5*24/25= 24 (area of the rhombus is 24)
