Nusret Balcı TMUA Paper 1 · Question 20

Consider a non-degenerate triangle with angles given by $x$ and $2x$ (measured in degrees). The side lengths of this triangle form a non-constant Geometric Progression (in some specific order).

Which of the following options correctly describes the number and location of all possible values for $x$ ?

AThere are no such values of

x

; such a triangle cannot exist.

BThere is exactly one value of

x

, and it lies in the interval

(30^\circ,36^\circ)

CThere is exactly one value of

x

, and it lies in the interval

(36^\circ,45^\circ)

DThere is exactly one value of

x

, and it lies in the interval

(45^\circ,60^\circ)

EThere are exactly two values of

x

: one in

(30^\circ,36^\circ)

and one in

(45^\circ,60^\circ)

FThere are exactly two values of

x

: one in

(36^\circ,45^\circ)

and one in

(45^\circ,60^\circ)

GThere are exactly two values of

x

: both lie in the interval

(36^\circ,45^\circ)

HThere are exactly three values of

x

: one in

(30^\circ,36^\circ)

, one in

(36^\circ,45^\circ)

, and one in

(45^\circ,60^\circ)

examday

Nusret Balcı TMUA Paper 1 · Q20