19N.2.SL.TZ0.S_6

pestleMathematicsAASLPaper 219N· sl-3-2-2d-and-3d-trig-sine-rule-cosine-rule-areasource ↗

The diagram below shows a triangular-based pyramid with base ${\text{ADC}}$ .
Edge ${\text{BD}}$ is perpendicular to the edges ${\text{AD}}$ and ${\text{CD}}$ .

${\text{AC}} = 28.4\,{\text{cm}}$ , ${\text{AB}} = x\,{\text{cm}}$ , ${\text{BC}} = x + 2\,{\text{cm}}$ , ${\text{A}}\widehat {\text{B}}{\text{C}} = 0.667$ , ${\text{B}}\widehat {\text{A}}{\text{D}} = 0.611$

Calculate ${\text{AD}}$

Markscheme / solution

evidence of choosing cosine rule (M1)

eg ${a^2} = {b^2} + {c^2} - 2bc\,{\text{cos}}\,A$

correct substitution to find ${\text{AB}}$ (A1)

eg ${28.4^2} = {x^2} + {\left( {x + 2} \right)^2} - 2x\left( {x + 2} \right){\text{cos}}\left( {0.667} \right)$

$x = 42.2822$ A2

appropriate approach to find ${\text{AD}}$ (M1)

eg ${\text{AD}} = x\,{\text{cos}}\left( {0.611} \right)$ , ${\text{cos}}\left( {0.611} \right) = \frac{{{\text{AD}}}}{{42.2822}}$

$34.6322$

${\text{AD}} = 34.6$ A1 N3

[6 marks]

Examiners’ report

[N/A]