If the sides of a triangle are in G...
Question
If the sides of a triangle are in GP and its larger angle is twice the smallest, then the common ratio saffer the inequality
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If the sides of a triangle are in GP and its larger angle is twice the smallest, then the common ratio saffer the inequality
(a) ( 0(b) (c) 1(d) r>sqrt{2} )

JEE/Engineering Exams
Maths
Solution
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If the sides of a triangle are in GP and its larger angle is twice the smallest, then the common ratior saffer the inequality
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 let sidu of ( lambda ) be ( frac{a}{gamma} ), a ( , a r)
[
4a> 0, f r>1
]
( frac{a}{r} ) is futclunt it it angli in of
ar is layent & ita auyl is 20
Now appluing sinc rule:
[
begin{array}{l}
frac{a / gamma}{sin theta}=frac{a gamma}{sin 2 sigma}
frac{1}{gamma sin theta}=frac{gamma}{2 sin theta cos theta} Rightarrow frac{gamma^{2}=2 cos theta}{3} mid gamma_{tan gamma}=sqrt{2}
end{array}
]
remer pow ( i eq mathbb{i} )
[
1<gamma<sqrt{2}
]
Option ( (b) )

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