9.1 Sine Rule - Set 1 Quiz

Report 1 / 5

In the diagram, \(LMN\) is a triangle.

Find the length of \(LN\).

Difficulty Level: Medium

Report 2 / 5

In the diagram, \(ABC\) is a triangle.

Find the length of \(BC\).

Difficulty Level: Medium

Report 3 / 5

Given a triangle \(ABC\) such that

\(\begin{aligned} AB&=6.2 \text{ cm}, \\\\ AC &=4.8 \text{ cm}, \\\\ &\text{ and} \\\\ \angle ABC&=43 ^\circ. \end{aligned}\)

Find the possible values of \(\begin{aligned} \angle BCA \end{aligned}\).

(A)		\(\begin{aligned} \angle BC_1A&=62.75 ^ \circ \\\\ \angle BC_2A&=119.25 ^\circ \end{aligned}\)

(B)		\(\begin{aligned} \angle BC_1A&=61.75 ^ \circ \\\\ \angle BC_2A&=118.25 ^\circ \end{aligned}\)

(C)		\(\begin{aligned} \angle BC_1A&=60.75 ^ \circ \\\\ \angle BC_2A&=117.25 ^\circ \end{aligned}\)

(D)		\(\begin{aligned} \angle BC_1A&=59.75 ^ \circ \\\\ \angle BC_2A&=116.25 ^\circ \end{aligned}\)

Difficulty Level: Medium

Report 4 / 5

Given a triangle \(DEF\) such that

\(\begin{aligned} DF&=6.5 \text{ cm}, \\\\EF &=6.9 \text{ cm}, \\\\ &\text{ and} \\\\ \angle FED&=68 ^\circ. \end{aligned}\)

Find the possible lengths of \(ED\).

(A)		\(\begin{aligned} ED_1 &=6. \, 735 \text{ cm} \\\\ ED_2 &=4. \, 435 \text{ cm} \end{aligned}\)

(B)		\(\begin{aligned} ED_1 &=5. \, 735 \text{ cm} \\\\ ED_2 &=3. \, 435 \text{ cm} \end{aligned}\)

(C)		\(\begin{aligned} ED_1 &=4. \, 735 \text{ cm} \\\\ ED_2 &=2. \, 435 \text{ cm} \end{aligned}\)

(D)		\(\begin{aligned} ED_1 &=3. \, 735 \text{ cm} \\\\ ED_2 &=1. \, 435 \text{ cm} \end{aligned}\)

Difficulty Level: Medium

Report 5 / 5

In a triangle \(GHI,\)

\(\begin{aligned} HI&=7.5 \text{ cm}, \\\\ GI &=5.6 \text{ cm}, \\\\ &\text{ and} \\\\ \angle IHG&=44 ^\circ. \end{aligned}\)

Find the possible values for \(\angle HGI\) and hence find the length of the remaining side of the acute-angled triangle \(GHI\).

Difficulty Level: Medium