Question

5

In the diagram, rhombus ABCD has sides of length 5 cm each and the length of the
diagonal AC is 8 cm.
(a) Find ABC
(b) Calculate the area of rhombus ABCD

Answer 1

a) the angle ABC is approximately 106 degrees b) 24

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)