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ABCD is a rhombus whose diagonals …

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ABCD is a rhombus whose diagonals AC makes an angle alpha with AB.If cos alpha = 2/3 and OB =3 cm find the length of the diagonal AC and BD

Posted by Amaan Rashid 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given :{tex}\cos \alpha = \frac { 2 } { 3 }{/tex}
and OB = 3 cm
In {tex}\triangle A O B{/tex} , {tex}\cos \alpha = \frac { 2 } { 3 } = \frac { A O } { A B }{/tex}
Let OA = 2x and AB = 3x
In {tex}\triangle A O B,{/tex}
{tex}AB^2=OA^2+OB^2{/tex}
(3x)² = (2x)²+ OB²
{tex}5x^2=OB^2=9{/tex}
{tex}x = \frac{3}{√5}{/tex}
So diagonal AC = 2OA = 4x = {tex}\frac {12}{√5} cm{/tex}
and diagonal BD = 2OB = 2 {tex}\times{/tex} 3 = 6 cm

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