Mathematics 0580 · IGCSE · Right-angled triangles

Right-angled triangles — practice question

The sketch depicts quadrilateral $ABCD$. Also, $AC = 12.3$ cm and $AD = 16.5$ cm. In addition, angle $BAC = 31^\circ$, angle $ABC = 90^\circ$ and angle $ACD = 90^\circ$.
(a)[2]

Show that $AB = 10.54$ cm, rounded to 2 decimal places.

(b)[2]

Show that angle $DAC = 41.80^\circ$, rounded to 2 decimal places.

(c)[3]

Calculate the length of $BD$.

(d)[4]

Calculate the value of angle $CBD$.

(e)[4]

Calculate the perpendicular distance from $C$ to $BD$.

Worked solution & mark scheme

This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hence, $\cos31^{\circ}=\dfrac{12.3}{AB}$

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