TMUA 2021 Paper 2 Q18 — Worked Solution

P2·Trigonometry, Logic & Quantifiers·7.0Official · 2021 · Q18

ambiguous-casesine-rulecase-analysis

A student chooses two distinct real numbers

x

and

y

with

0 < x < y < 1

.The student then attempts to draw a triangle

A B C

with

A B = 1, sin A = x, sin B = y .

(Note that congruent triangles are considered to be the same.)Which of the following statements is/are correct?

For some choice of

x

and

y

, there is exactly one triangle the student could draw.

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.

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