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

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} )
Solution

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) )