Pre-U Pre-U 9794/2 2013 November — Question 4

Exam BoardPre-U
ModulePre-U 9794/2 (Pre-U Mathematics Paper 2)
Year2013
SessionNovember
TopicSine and Cosine Rules
TypePerpendicular from vertex
DifficultyStandard +0.3 This is a straightforward two-part sine rule application. Part (i) uses sine rule to find an angle (with the obtuse specification removing ambiguity), and part (ii) requires recognizing that 'shortest distance' means perpendicular height, calculated via area or simple trigonometry. Both parts are standard techniques with no novel insight required, making this slightly easier than average.
Spec1.05b Sine and cosine rules: including ambiguous case

4 The diagram shows a triangle \(A B C\) in which \(A B = 5 \mathrm {~cm} , B C = 10 \mathrm {~cm}\) and angle \(B C A = 20 ^ { \circ }\). \includegraphics[max width=\textwidth, alt={}, center]{f4e774e5-76fd-48ff-9bce-a995b3ba517b-2_355_767_1695_689}
  1. Find angle \(B A C\), given that it is obtuse.
  2. Find the shortest distance from \(A\) to \(B C\).

4 The diagram shows a triangle $A B C$ in which $A B = 5 \mathrm {~cm} , B C = 10 \mathrm {~cm}$ and angle $B C A = 20 ^ { \circ }$.\\
\includegraphics[max width=\textwidth, alt={}, center]{f4e774e5-76fd-48ff-9bce-a995b3ba517b-2_355_767_1695_689}\\
(i) Find angle $B A C$, given that it is obtuse.\\
(ii) Find the shortest distance from $A$ to $B C$.

\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2013 Q4}}