Find lengths of diagonals AC and BD. Given AB = 60 cm and ∠BAD = 60°.

Question

KnowledgeBoat · Accepted Answer

ABCD is a rhombus as AB = BC = CD = DA and ∠ BAD = 60°. Now in Δ ABD, AB = AD (Sides of rhombus) ⇒ ∠ ABD = ∠ ADB (Angles opposite to equal side of Δ) Let ∠ ABD = `x`. According to the angle sum property, ∠ ABD \+ ∠ ADB \+ ∠ BAD = 180° ⇒ x \+ x \+ 60° = 180° ⇒ 2x \+ 60° = 180° ⇒ 2x = 180° \- 60° ⇒ 2x = 120° ⇒ x = ⇒ x = 60° ABCD is a rhombus. So, diagonals AC and BD bisect each other at 90°. AO = OC and BO = OD In Δ AOD, And, AC = 2 x AO = 2 x 51.96 = 103.92 cm BD = 2 x BO = 2 x 30 = 60 cm Hence, AC = 103.92 cm and BD = 60 cm.

Mathematics

Find lengths of diagonals AC and BD.
Given AB = 60 cm and ∠BAD = 60°.

Trigonometric Identities

Related Questions

Find AD, if :

Find the length of AD.
Given :
∠ABC = 60°,
∠DBC = 45°
and BC = 40 cm.

Find AB.

In trapezium ABCD, as shown, AB // DC, AD = DC = BC = 20 cm and ∠A = 60°.
Find :
(i) length of AB
(ii) distance between AB and DC.