: Solving geometric problems using trigonometry
Q.4.4 The sides of a rhombus are 7 centimetre long and one of its angles is 400
. Calculate its area
(sin 400
= 0.643, cos 400
= 0.766, tan 400
= 0.839)
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Answer:
(i) It is given that
Area of rhombus = 480 cm
2
It can be written as
2
1
×d
1
×d
2
=480
So we get
2
1
×48×d
2
=480
On further calculation
d
2
= 20cm
(ii) Consider AC = 48cm and BD = 20cm
The diagonals of a rhombus bisect at right angles
Consider Δ AOD,
Using the Pythagoras theorem
AD
2
=OD
2
+AO
2
By substituting the values
AD
2
=24
2
+10
2
On further calculation
AD
2
=576+100
By addition
AD
2
=676
By taking out the square root
AD=
676
So we get
AD = 26 cm
We know that AD = BC = CD = AD = 26 m
Therefore, the length of each side of rhombus is 26cm.
(iii) We know that
Perimeter of a rhombus = 4 (side)
By substituting the value of side from above
Perimeter of a rhombus = 4 (26)
So we get
Perimeter of a rhombus = 104 cm
solution
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