Perpendicular from vertex

A question is this type if and only if it requires finding the perpendicular distance from a vertex to the opposite side, typically using area or trigonometry after finding other triangle properties.

4 questions · Moderate -0.1

1.05b Sine and cosine rules: including ambiguous case
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OCR MEI C2 Q6
5 marks Standard +0.3
6 A and B are points on the same side of a straight river. A and B are 180 metres apart. The angles made with a jetty J on the opposite side of the river \(78 ^ { \circ }\) and \(56 ^ { \circ }\) respectively as shown. \includegraphics[max width=\textwidth, alt={}, center]{c55a5f04-3573-4f36-a12c-3755bdd4a45b-3_332_681_1451_565} Not to scale Calculate the width of the river correct to the nearest metre.
AQA C2 2011 January Q3
8 marks Moderate -0.3
3 The triangle \(A B C\), shown in the diagram, is such that \(A B = 5 \mathrm {~cm} , A C = 8 \mathrm {~cm}\), \(B C = 10 \mathrm {~cm}\) and angle \(B A C = \theta\).
  1. Show that \(\theta = 97.9 ^ { \circ }\), correct to the nearest \(0.1 ^ { \circ }\).
    1. Calculate the area of triangle \(A B C\), giving your answer, in \(\mathrm { cm } ^ { 2 }\), to three significant figures.
    2. The line through \(A\), perpendicular to \(B C\), meets \(B C\) at the point \(D\). Calculate the length of \(A D\), giving your answer, in cm , to three significant figures.
AQA C2 2008 June Q4
8 marks Moderate -0.8
4 The diagram shows a triangle \(A B C\). \includegraphics[max width=\textwidth, alt={}, center]{a2525df8-dbd0-4b69-b6bb-f8ef6f96f7dc-3_394_522_1062_751} The size of angle \(B A C\) is \(65 ^ { \circ }\), and the lengths of \(A B\) and \(A C\) are 7.6 m and 8.3 m respectively.
  1. Show that the length of \(B C\) is 8.56 m , correct to three significant figures.
  2. Calculate the area of triangle \(A B C\), giving your answer in \(\mathrm { m } ^ { 2 }\) to three significant figures.
  3. The perpendicular from \(A\) to \(B C\) meets \(B C\) at the point \(D\). Calculate the length of \(A D\), giving your answer to the nearest 0.1 m .
Pre-U Pre-U 9794/2 2013 November Q4
Standard +0.3
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 \(B C\).