Mathematics 0580 · IGCSE · Non-right-angled triangles

Non-right-angled triangles — practice question

The figure depicts triangle $ABC$.
(a(i))[4]

Use the cosine rule to find $BC$.

(a(ii))[3]

Use the sine rule to find angle $ACB$.

(b(i))[4]

Triangle $DEF$ has area $70\text{ m}^2$. Show that $4x^2 + 11x - 300 = 0$.

(b(ii))[4]

Use the quadratic formula to solve $4x^2 + 11x - 300 = 0$. Show all your working and give your answers rounded to 2 decimal places.

(b(iii))[1]

Find the length of $DE$.

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