Question no 18
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18. In a rhombus ABCD, diagonals AC and BD intersect at point O. If cosine of angle CAB is 0.6 and length of OB is 8 cm, find length of sides and diagonals of rhombus.
Given
- cos∅ = 0.6
- OB = 8 cm
Solution
→ cos∅ = Base/Hypotenuse
→ 0.6 = 8/H
→ H = 80/6
→ Hypotenuse = 13.3 cm
→ 13.3² = 8² + P²
→ 176.89 - 64 = P²
→ 10.62 = Perpendicular
Diagonals = 2OA and 2OB
→ D = 2(10.62) and 2(8)
→ Diagonals = 21.24 and 16 cm.
Hence length of each side is 13.3 cm and diagonals is 21.24 cm and 16 cm.
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