Question

18. In rhombus ABCD, diagonals AC and BD
intersect each other at point O.
If cosine of angle CAB is 0.6 and
OB = 8 cm, find the lengths of the side and
the diagonals of the rhombus.​

Answer 1

Answer:

The diagonals of a Rhombus bisect each other perpendicularly

cos angle CAB=6/10=3/5

i.e., base/hypotenuse =OA/AB=3/5

Therefore, if length of base =3x, length of hypotenuse=5x

Since,

(OB)^2+(OA)^2=(AB)^2 (USING PYTHAGORAS THEROEM)

(OA)^2-(AB)^2=(OB)^2

(5x)^2-(3x)^2=(OB)^2

(OB)^2=16x^2

therefore,

OB=4x

Now, OB=8

4x=8

x=8/4

x=2

Therefore,

AB=5x

=5×2

=10cm

AND

OA=3x

=3×2

=6cm

Since the sides of a rhombus are equal.So, the length of the side of the rhombus.

The diagonals are:

BD=8×2

=16cm

AC=6×2

=12cm

HOPE THIS HELP U