Foundation November 2024 Paper 1 Q27

eg \(51^2 = (DE)^2 + 24^2\) oe or \(2601 = (DE)^2 + 576\) oe

or \((DE^2 =)\;51^2 - 24^2\;(= 2025)\) oe or \((DE^2 =)\;2601 - 576\;(= 2025)\) oe or

\(\cos(DFE) = \dfrac{24}{51}\) or \(\sin(DEF) = \dfrac{24}{51}\)

\((DE =)\sqrt{51^2 - 24^2}\;\left(= \sqrt{2025} = 45\right)\) or \((DE =)\sqrt{2601 - 576}\;\left(= \sqrt{2025} = 45\right)\)

or \((DFE =)\cos^{-1}\left(\dfrac{24}{51}\right)(= 61.9\ldots)\) or \((DEF =)\sin^{-1}\left(\dfrac{24}{51}\right)(= 28.0\ldots)\)

\(\dfrac{\textit{their } DE}{7.5}(= 6)\) oe or \(\dfrac{7.5}{\textit{their } DE}\left(= \dfrac{1}{6}\right)\) or \(\dfrac{x}{24} = \dfrac{7.5}{\textit{their } DE}\) oe

or \(\tan\text{“}\textit{their } 61.9\ldots\text{”} = \dfrac{7.5}{(x)}\) or \(\tan\text{“}\textit{their } 28.0\ldots\text{”} = \dfrac{(x)}{7.5}\) or

\(\dfrac{(x)}{\sin(\textit{their } 28.0)} = \dfrac{7.5}{\sin(\textit{their } 61.9)}\)

NB Their \(ED\) or their 61.9 or their 28.0 must be clearly identified

Their 61.9.. or their 28.0.. cannot be used as lengths of the triangle

Their 45 cannot be used as an angle of the triangle

\(24 \div\) “6” oe or \(24 \times \text{“}\dfrac{1}{6}\text{”}\) or 24 × “1.67” or \((x =)\;\dfrac{7.5}{\textit{their } ED} \times 24\)

or \((x =)\;\dfrac{7.5}{\tan\text{“}\textit{their } 61.9\ldots\text{”}}\) oe or \((x =)\;7.5 \times \tan\text{“}\textit{their } 28.0\ldots\text{”}\) oe

or \((x =)\;\dfrac{7.5}{\sin(\textit{their } 61.9)} \times \sin(\textit{their } 28.0)\) oe

or \(51 \times \text{“}\dfrac{1}{6}\text{”}\;(= 8.5)\) and \((x =)\sqrt{8.5^2 - 7.5^2}\;\left(= \sqrt{16}\right)\)