Question

11.One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus,

Answer 1

If one diagonal equals side if rhombus , and we suppose side of rhombus as s

then , a right angled triangle will be formed at the centre from rhombus

So , ( s/2 )² + ( z/2 )² = s²

z² = 4 ( s² - s²/4 )

z² = 4 ( 3s² / 4 )

z² = 3 s²

z = s√3

So , we got some information

d1 = s

d2 = s√3

side = s

Angle in one triangle made by half-half diagonals of rhombus

sin Φ = ( s√3 / 2 ) / ( s )

sin Φ = √3 /2

Φ = 60°

Then , another triangle made by half-half diagonals

sin Φ = ( s√3 / 2 ) / ( s )

sin Φ = √3 /2

Φ = 60°

Ultimately , two of them wills um to form 120°

Now , adjacent to 120° is 180° - 120° = 60°

And, oppsite to .120° is 120°

Now , Resultant is 60° , 120° , 60° , 120° .