(a)[2]
Determine the height of the post.
(b)[4]
Use the cosine rule to determine angle $BAC$.
(c)[3]
Use the sine rule to determine angle $CAD$.
(d)[3]
Calculate the area of the field.
(e)[2]
Find the bearing of $A$ as seen from $C$.
Mathematics 0580 · IGCSE · Non-right-angled triangles
Non-right-angled triangles — practice question
The sketch depicts a field, $ABCD$, on level ground. The sides are marked as $AB = 158\text{ m}$, $BC = 107\text{ m}$, $CD = 86\text{ m}$, and the diagonal $AC = 132\text{ m}$. The angle at $D$ is $116^\circ$. A north arrow is drawn at $A$. Diagram not to scale.