Point on side of triangle

A question is this type if and only if a point lies on one side of a triangle creating two sub-triangles, requiring separate calculations in each sub-triangle.

8 questions · Standard +0.0

1.05b Sine and cosine rules: including ambiguous case
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OCR MEI C2 Q3
5 marks Moderate -0.3
3 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cd507fa5-97b2-4edd-ae37-a58aea1de5ed-3_596_689_244_534} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure} \section*{Not to scale} In Fig. 3, BCD is a straight line. \(\mathrm { AC } = 9.8 \mathrm {~cm} , \mathrm { BC } = 7.3 \mathrm {~cm}\) and \(\mathrm { CD } = 6.4 \mathrm {~cm}\); angle \(\mathrm { ACD } = 53.4 ^ { \circ }\).
  1. Calculate the length AD .
  2. Calculate the area of triangle ABC .
OCR MEI C2 Q6
5 marks Standard +0.3
6
Not to scale \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cd507fa5-97b2-4edd-ae37-a58aea1de5ed-5_484_968_1516_617} \captionsetup{labelformat=empty} \caption{Fig. 7}
\end{figure} Fig. 7 shows triangle ABC , with \(\mathrm { AB } = 8.4 \mathrm {~cm}\). D is a point on AC such that angle \(\mathrm { ADB } = 79 ^ { \circ }\), \(\mathrm { BD } = 5.6 \mathrm {~cm}\) and \(\mathrm { CD } = 7.8 \mathrm {~cm}\). Calculate
  1. angle BAD ,
  2. the length BC .
OCR C2 2011 June Q1
7 marks Standard +0.3
1 The diagram shows triangle \(A B C\), with \(A B = 9 \mathrm {~cm} , A C = 17 \mathrm {~cm}\) and angle \(B A C = 40 ^ { \circ }\).
  1. Find the length of \(B C\).
  2. Find the area of triangle \(A B C\).
  3. \(D\) is the point on \(A C\) such that angle \(B D A = 63 ^ { \circ }\). Find the length of \(B D\).
OCR C2 2014 June Q1
6 marks Standard +0.3
1 \includegraphics[max width=\textwidth, alt={}, center]{9e95415c-00f5-4b52-a443-0b946602b3b4-2_426_1244_280_413} The diagram shows triangle \(A B C\), with \(A B = 8 \mathrm {~cm}\), angle \(B A C = 65 ^ { \circ }\) and angle \(B C A = 30 ^ { \circ }\). The point \(D\) is on \(A C\) such that \(A D = 10 \mathrm {~cm}\).
  1. Find the area of triangle \(A B D\).
  2. Find the length of \(B D\).
  3. Find the length of \(B C\).
OCR MEI C2 2012 June Q3
5 marks Moderate -0.3
3 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8f7413d8-2814-4d5c-bec0-ce118fec80eb-2_592_693_845_502} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure} \section*{Not to scale} In Fig. 3, BCD is a straight line. \(\mathrm { AC } = 9.8 \mathrm {~cm} , \mathrm { BC } = 7.3 \mathrm {~cm}\) and \(\mathrm { CD } = 6.4 \mathrm {~cm}\); angle \(\mathrm { ACD } = 53.4 ^ { \circ }\).
  1. Calculate the length AD .
  2. Calculate the area of triangle ABC .
AQA C2 2015 June Q2
7 marks Moderate -0.3
2 The diagram shows a triangle \(A B C\). The size of angle \(B A C\) is \(72 ^ { \circ }\) and the size of angle \(A B C\) is \(48 ^ { \circ }\). The length of \(B C\) is 20 cm .
  1. Show that the length of \(A C\) is 15.6 cm , correct to three significant figures.
  2. The midpoint of \(B C\) is \(M\). Calculate the length of \(A M\), giving your answer, in cm , to three significant figures.
    [0pt] [4 marks]
OCR MEI Paper 3 2021 November Q11
5 marks Challenging +1.2
11 In this question you must show detailed reasoning. The diagram shows triangle ABC , with \(\mathrm { BC } = 8 \mathrm {~cm}\) and angle \(\mathrm { BAC } = 45 ^ { \circ }\).
The point D on AC is such that \(\mathrm { DC } = 5 \mathrm {~cm}\) and \(\mathrm { BD } = 7 \mathrm {~cm}\). \includegraphics[max width=\textwidth, alt={}, center]{a0d9573f-8273-4562-a2d3-07f15d9da1af-7_684_553_1119_258} Determine the exact length of AB .
OCR MEI C2 2010 January Q7
5 marks Moderate -0.8
\includegraphics{figure_7} Fig. 7 shows triangle ABC, with AB = 8.4 cm. D is a point on AC such that angle ADB = 79°, BD = 5.6 cm and CD = 7.8 cm. Calculate
  1. angle BAD, [2]
  2. the length BC. [3]