TMUA Official 2021 Paper 2 · Question 18

A student chooses two distinct real numbers $x$ and $y$ with $0<x<y<1$ .

The student then attempts to draw a triangle $ABC$ with:

\begin{aligned}AB&=1\\\sin A&=x\\\sin B&=y.\end{aligned}

Which of the following statements is/are correct?

I. For some choice of $x$ and $y$ , there is exactly one triangle the student could draw.
II. For some choice of $x$ and $y$ , there are exactly two different triangles the student could draw.
III. For some choice of $x$ and $y$ , there are exactly three different triangles the student could draw.

(Note that congruent triangles are considered to be the same.)

Anone of them

BI only

CII only

DIII only

EI and II only

FI and III only

GII and III only

HI, II and III

examday