tmua 2023 Q8

tmua · Uk · paper1 1 marks Sine and Cosine Rules Ambiguous case and triangle existence/uniqueness

A triangle $X Y Z$ is called fun if it has the following properties:
$$\begin{aligned} & \text { angle } Y X Z = 30 ^ { \circ } \\ & X Y = \sqrt { 3 } a \\ & Y Z = a \end{aligned}$$
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 $T$

..... 10

A triangle $X Y Z$ is called fun if it has the following properties:

$$\begin{aligned}
& \text { angle } Y X Z = 30 ^ { \circ } \\
& X Y = \sqrt { 3 } a \\
& Y Z = a
\end{aligned}$$

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 $T$

Paper Questions

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