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) )