Questions
The acute angle of a rhombus whose side is a mean proportion al between its diagonals is
a
15°
b
20°
c
30°
d
80°
detailed solution
Correct option is C
Let the length of the diagonals of the rhombus be a and b and x be its side then xa=bx⇒x2=ab Now cosθ=x2+x2−a22x⋅x=2ab−a22ab=1−a2b Similarly cos180∘−θ=1−b2a⇒a2b=1−cosθ,b2a=1+cosθ⇒1−cos2θ=14⇒sinθ=12⇒θ=30∘Talk to our academic expert!
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If then the value of is equal to
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