Question
ABCD is a quadrilateral where \({\text{AB}} = 6.5,{\text{ BC}} = 9.1,{\text{ CD}} = 10.4,{\text{ DA}} = 7.8\) and \({\rm{C\hat DA}} = 90^\circ \). Find \({\rm{A\hat BC}}\), giving your answer correct to the nearest degree.
▶️Answer/Explanation
Markscheme
\({\text{A}}{{\text{C}}^2} = {7.8^2} + {10.4^2}\) (M1)
\({\text{AC}} = 13\) (A1)
use of cosine rule eg, \(\cos ({\rm{A\hat BC}}) = \frac{{{{6.5}^2} + {{9.1}^2} – {{13}^2}}}{{2(6.5)(9.1)}}\) M1
\({\rm{A\hat BC}} = 111.804 \ldots ^\circ {\text{ }}( = 1.95134 \ldots )\) (A1)
\( = 112^\circ \) A1
[5 marks]
Examiners report
Well done by most candidates. A small number of candidates did not express the required angle correct to the nearest degree.