Mathematics 4024 · O Level · Non-right-angled triangles

Non-right-angled triangles — practice question

For triangle $ABC$, $BC = 16\text{ cm}$ and $\angle BAC = 60^\circ$. The length of $AB$ is $x\text{ cm}$, and $AC$ measures $2x + 3\text{ cm}$.
(a(i))[1]

Evaluate the numerical value of $\frac{8\sin 54^\circ}{\sin 18^\circ}$.

(a(ii))[1]

Calculate $\sqrt{4.73^2 - 1.65\sin 43^\circ}$.

(b(i))[4]

Form an equation in $x$ and show that it reduces to $3x^2 + 9x - 247 = 0$.

(b(ii))[3]

Solve $3x^2 + 9x - 247 = 0$, giving your answers correct to $2$ decimal places.

(b(iii))[1]

Hence state the lengths of $AB$ and $AC$.

(b(iv))[2]

Determine the area of triangle $ABC$.

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