OCR C2 2005 January — Question 3 7 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2005
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSine and Cosine Rules
TypeBearings and navigation
DifficultyStandard +0.3 This is a straightforward application of sine rule and basic trigonometry in triangles. Students need to find angle ALB (35°), use sine rule to find LB, then use right-angled triangle for perpendicular distance, and finally apply sine/cosine rule in triangle LBC. While it requires multiple steps (4-5 marks typical), each step follows standard procedures with no novel insight needed, making it slightly easier than average.
Spec1.05b Sine and cosine rules: including ambiguous case

3 \includegraphics[max width=\textwidth, alt={}, center]{608720b6-5b18-45e9-8838-c94b347ab3b7-2_488_604_895_769} A landmark \(L\) is observed by a surveyor from three points \(A , B\) and \(C\) on a straight horizontal road, where \(A B = B C = 200 \mathrm {~m}\). Angles \(L A B\) and \(L B A\) are \(65 ^ { \circ }\) and \(80 ^ { \circ }\) respectively (see diagram). Calculate
  1. the shortest distance from \(L\) to the road,
  2. the distance \(L C\).

3\\
\includegraphics[max width=\textwidth, alt={}, center]{608720b6-5b18-45e9-8838-c94b347ab3b7-2_488_604_895_769}

A landmark $L$ is observed by a surveyor from three points $A , B$ and $C$ on a straight horizontal road, where $A B = B C = 200 \mathrm {~m}$. Angles $L A B$ and $L B A$ are $65 ^ { \circ }$ and $80 ^ { \circ }$ respectively (see diagram). Calculate\\
(i) the shortest distance from $L$ to the road,\\
(ii) the distance $L C$.

\hfill \mbox{\textit{OCR C2 2005 Q3 [7]}}