If the length of each side of a rhombus is 8 cm and its one angle is 60°, then find the lengths of the diagonals of the rhombus.

We know that the diagonals of a rhombus bisect the opposite angles and are perpendicular to each other. ∴ ∠OAB = = 30°. In right ∠AOB, ⇒ sin 30° = ⇒ ⇒ OB = ⇒ OB = = 4 cm. As diagonals of rhombus bisect each other. ∴ BD = 2 OB = 2 × 4 = 8 cm. cos 30° = ⇒ ⇒ OA = ⇒ OA = . As diagonals of rhombus bisect each other. ∴ AC = 2 OA = . Hence, the length of the diagonals of the rhombus are 8 cm and cm.

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In the right-angled triangle ABC, ∠C = 90° and ∠B = 60°. If AC = 6 cm, find the lengths of the sides BC and AB.

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If sin x + cos y = 1, x = 30° and y is acute angle, find the value of y.

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In the adjoining figure, AP is a man of height 1.8 m and BQ is a building 13.8 m high. If the man sees the top of the building by focussing his binoculars at an angle of 30° to the horizontal, find the distance of the man from the building.

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Mathematics

If the length of each side of a rhombus is 8 cm and its one angle is 60°, then find the lengths of the diagonals of the rhombus.

Trigonometrical Ratios

Related Questions

In the right-angled triangle ABC, ∠C = 90° and ∠B = 60°. If AC = 6 cm, find the lengths of the sides BC and AB.

If sin x + cos y = 1, x = 30° and y is acute angle, find the value of y.

In the adjoining figure, AP is a man of height 1.8 m and BQ is a building 13.8 m high. If the man sees the top of the building by focussing his binoculars at an angle of 30° to the horizontal, find the distance of the man from the building.