Mathematics 4024 · O Level · Pythagoras' theorem and trigonometry in 3D

Pythagoras' theorem and trigonometry in 3D — practice question

Applying trigonometry to triangles and pyramids.
(a(i))[3]

For triangle $ABC$, $AC = 6.4\text{ cm}$, $BC = 9.5\text{ cm}$ and $\angle BAC = 79^{\circ}$. Calculate $\angle ABC$.

(a(ii))[3]

Calculate the area for triangle $ABC$.

(b(i))[3]

In pyramid $ABCD$, triangle $ABC$ is the horizontal base. If $BD = 9.8\text{ cm}$ and $CD = 8.2\text{ cm}$, with $\angle BAD = \angle CAD = 90^{\circ}$, calculate $\angle BDC$.

(b(ii))[2]

Calculate the elevation angle of $D$ as seen from $C$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: $41.4^{\circ}$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI