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.

Question

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.

KnowledgeBoat · Accepted Answer

As we know that the diagonals of a rhombus bisect each other at right angles. cos ∠CAB = 0.6 = cos ∠CAB = ∴ If length of OA = 3x cm, length of AB = 5x cm. In Δ ABO, ⇒ AB2 = AO2 \+ BO2 (∵ AB is hypotenuse) ⇒ (5x)2 = (3x)2 \+ BO2 ⇒ 25x2 = 9x2 \+ BO2 ⇒ BO2 = 25x2 \- 9x2 ⇒ BO2 = 16x2 ⇒ BO = ⇒ BO = 4x It is given that OB = 8 cm So, 4x = 8 x = Therefore, OA = 3x = 3 x 2 = 6 cm and AB = 5x = 5 x 2 cm = 10 cm. Diagonal BD = 2 x OB = 2 x 8 cm = 16 cm Diagonal AC = 2 x OA = 2 x 6 cm = 12 cm Hence, diagonals = 16 cm and 12 cm and side = 10 cm.

Mathematics

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.

Trigonometric Identities

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Mathematics

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.

Trigonometric Identities

Related Questions

If sec (90° - 3A).cos 48° = 1 and 0 ≤ 3A ≤ 90°; find the value of angle A.

In △ABC, angle C is 90° then find the value of sin (A + B).

If sec A sin A = 0, find the value of cos A.

Find angle A, if sec 2A = cosec (A + 48°).

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.