TMUA 2023 Paper 1 Q8 — Worked Solution

P1·Trigonometry·5.5Official · 2023 · Q8

cosine-ruleambiguous-trianglearea-ratio

A triangle

X Y Z

is called fun if it has the following properties:

∠ Y X Z = 3 0^{\circ}, X Y = 3 a, Y Z = a,

where

a

is a constant.For a given value of

a

, there are two distinct fun triangles

S

and

T

, where the area of

S

is greater than the area of

T

. Find the ratio

area of S : area of T .

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