Question

Work out the length x in the triangle below. If your answer is a decimal, give it to 1 d.p.

area = 42 m²

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Answer 1

The length of side x in the given triangle is 12 m.

Explanation:

To calculate length x in the given triangle, use the Area Sine Rule.

`\boxed{\begin{minipage}{7.6 cm}\underline{Area Sine Rule} \\\\$A=(1)/(2)ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides enclosing the angle. \\\end{minipage}}`

The given values are:

• a = 14 m
• b = x
• C = 30°
• A = 42 m²

Substitute the given values into the formula:

`\implies 42=(1)/(2) \cdot 14 \cdot x\cdot \sin30^(\circ)`

Multiply 1/2 · 14 = 7:

`\implies 42=7x\sin30^(\circ)`

Divide both sides of the equation by 7:

`\implies 6=x\sin30^(\circ)`

Calculate sin30°:

`\implies 6=(1)/(2)x`

Multiply both sides of the equation by 2:

`\implies 12=x`

Therefore, the length of side x in the given triangle is 12 m.