Sequential triangle calculations (basic)

A question is this type if and only if it requires solving 2-3 parts of a single triangle sequentially (e.g., find an angle using cosine rule, then find area, or find a side then find an angle), without additional geometric elements.

20 questions · Moderate -0.9

1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C)
Sort by: Default | Easiest first | Hardest first
Edexcel C2 2011 January Q2
6 marks Moderate -0.8
2. In the triangle \(A B C , A B = 11 \mathrm {~cm} , B C = 7 \mathrm {~cm}\) and \(C A = 8 \mathrm {~cm}\).
  1. Find the size of angle \(C\), giving your answer in radians to 3 significant figures.
  2. Find the area of triangle \(A B C\), giving your answer in \(\mathrm { cm } ^ { 2 }\) to 3 significant figures.
OCR C2 2006 January Q2
6 marks Moderate -0.8
2 Triangle \(A B C\) has \(A B = 10 \mathrm {~cm} , B C = 7 \mathrm {~cm}\) and angle \(B = 80 ^ { \circ }\). Calculate
  1. the area of the triangle,
  2. the length of \(C A\),
  3. the size of angle \(C\).
OCR MEI C2 2005 January Q4
5 marks Moderate -0.8
4 Fig. 4 For triangle ABC shown in Fig. 4, calculate
  1. the length of BC ,
  2. the area of triangle ABC .
OCR C2 Q2
5 marks Moderate -0.8
2. The diagram shows triangle \(A B C\) in which \(A B = 12.6 \mathrm {~cm} , \angle A B C = 107 ^ { \circ }\) and \(\angle A C B = 31 ^ { \circ }\). Find
  1. the length \(B C\),
  2. the area of triangle \(A B C\).
OCR C2 2013 January Q1
4 marks Moderate -0.8
1 The diagram shows triangle \(A B C\), with \(A C = 14 \mathrm {~cm} , B C = 10 \mathrm {~cm}\) and angle \(A B C = 63 ^ { \circ }\).
  1. Find angle \(C A B\).
  2. Find the length of \(A B\).
OCR C2 2009 June Q1
5 marks Moderate -0.8
1 The lengths of the three sides of a triangle are \(6.4 \mathrm {~cm} , 7.0 \mathrm {~cm}\) and 11.3 cm .
  1. Find the largest angle in the triangle.
  2. Find the area of the triangle.
OCR PURE Q1
7 marks Easy -1.2
1 In the triangle \(A B C , A B = 3 , B C = 4\) and angle \(A B C = 30 ^ { \circ }\). Find the following.
  1. The area of the triangle.
  2. The length \(A C\).
  3. The angle \(A C B\).
AQA C2 2008 January Q3
6 marks Easy -1.2
3 The diagram shows a triangle \(A B C\). The length of \(A C\) is 18.7 cm , and the sizes of angles \(B A C\) and \(A B C\) are \(72 ^ { \circ }\) and \(50 ^ { \circ }\) respectively.
  1. Show that the length of \(B C = 23.2 \mathrm {~cm}\), correct to the nearest 0.1 cm .
  2. Calculate the area of triangle \(A B C\), giving your answer to the nearest \(\mathrm { cm } ^ { 2 }\).
AQA C2 2009 January Q3
7 marks Moderate -0.8
3 The diagram shows a triangle \(A B C\).
[diagram]
The size of angle \(A\) is \(63 ^ { \circ }\), and the lengths of \(A B\) and \(A C\) are 7.4 m and 5.26 m respectively.
  1. Calculate the area of triangle \(A B C\), giving your answer in \(\mathrm { m } ^ { 2 }\) to three significant figures.
  2. Show that the length of \(B C\) is 6.86 m , correct to three significant figures.
  3. Find the value of \(\sin \boldsymbol { B }\) to two significant figures.
AQA C2 2005 June Q1
5 marks Moderate -0.8
1 The diagram shows a triangle \(A B C\). \includegraphics[max width=\textwidth, alt={}, center]{37627fc4-a90b-4f3b-9b10-0a9e200f8485-2_423_707_612_657} The lengths of \(A C\) and \(B C\) are 5 cm and 4.8 cm respectively.
The size of the angle \(B C A\) is \(30 ^ { \circ }\).
  1. Calculate the area of the triangle \(A B C\).
  2. Calculate the length of \(A B\), giving your answer to three significant figures.
AQA C2 2006 June Q2
6 marks Easy -1.2
2 The diagram shows a triangle \(A B C\). \includegraphics[max width=\textwidth, alt={}, center]{f066f68a-e739-4da3-8ec1-e221461146b0-2_757_558_1409_726} The lengths of \(A C\) and \(B C\) are 4.8 cm and 12 cm respectively.
The size of the angle \(B A C\) is \(100 ^ { \circ }\).
  1. Show that angle \(A B C = 23.2 ^ { \circ }\), correct to the nearest \(0.1 ^ { \circ }\).
  2. Calculate the area of triangle \(A B C\), giving your answer in \(\mathrm { cm } ^ { 2 }\) to three significant figures.
AQA C2 2010 June Q3
6 marks Easy -1.2
3 The triangle \(A B C\), shown in the diagram, is such that \(A B = 6 \mathrm {~cm} , B C = 15 \mathrm {~cm}\), angle \(B A C = 150 ^ { \circ }\) and angle \(A C B = \theta\). \includegraphics[max width=\textwidth, alt={}, center]{f9a7a4dd-f7fd-4135-8872-2c1270d46a14-4_376_867_406_584}
  1. Show that \(\theta = 11.5 ^ { \circ }\), correct to the nearest \(0.1 ^ { \circ }\).
  2. Calculate the area of triangle \(A B C\), giving your answer in \(\mathrm { cm } ^ { 2 }\) to three significant figures.
AQA C2 2011 June Q1
6 marks Moderate -0.8
1 The triangle \(A B C\), shown in the diagram, is such that \(A C = 9 \mathrm {~cm} , B C = 10 \mathrm {~cm}\), angle \(A B C = 54 ^ { \circ }\) and the acute angle \(B A C = \theta\).
  1. Show that \(\theta = 64 ^ { \circ }\), correct to the nearest degree.
  2. Calculate the area of triangle \(A B C\), giving your answer to the nearest square centimetre.
AQA C2 2014 June Q1
5 marks Easy -1.2
1 The diagram shows a triangle \(A B C\). The size of angle \(B A C\) is \(47 ^ { \circ }\) and the lengths of \(A B\) and \(A C\) are 5 cm and 12 cm respectively.
  1. Calculate the area of the triangle \(A B C\), giving your answer to the nearest \(\mathrm { cm } ^ { 2 }\).
  2. Calculate the length of \(B C\), giving your answer, in cm , to one decimal place.
    [0pt] [3 marks]
Edexcel C2 Q1
5 marks Easy -1.2
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{089f5506-94ac-489f-b219-e67fa6ca834f-2_383_707_246_488} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows triangle \(A B C\) in which \(A B = 12.6 \mathrm {~cm} , \angle A B C = 107 ^ { \circ }\) and \(\angle A C B = 31 ^ { \circ }\).
Find, to 3 significant figures,
  1. the length \(B C\),
  2. the area of triangle \(A B C\).
Pre-U Pre-U 9794/2 2014 June Q1
2 marks Easy -1.2
1 The diagram shows the triangle \(A B C\). \(A B = 10 \mathrm {~cm} , A C = 7 \mathrm {~cm}\) and angle \(B A C = 100 ^ { \circ }\).
  1. Find the length \(B C\).
  2. Find the area of the triangle \(A B C\).
Pre-U Pre-U 9794/1 2017 June Q3
6 marks Moderate -0.8
3 A triangle \(A B C\) has sides \(A B , B C\) and \(C A\) of lengths \(7 \mathrm {~cm} , 6 \mathrm {~cm}\) and 8 cm respectively.
  1. Show that \(\cos A B C = \frac { 1 } { 4 }\).
  2. Find the area of triangle \(A B C\).
AQA C2 2009 June Q1
5 marks Moderate -0.8
The triangle \(ABC\), shown in the diagram, is such that \(AB = 7\) cm, \(AC = 5\) cm, \(BC = 8\) cm and angle \(ABC = \theta\). \includegraphics{figure_1}
  1. Show that \(\theta = 38.2°\), correct to the nearest \(0.1°\). [3]
  2. Calculate the area of triangle \(ABC\), giving your answer, in cm\(^2\), to three significant figures. [2]
OCR C2 2007 January Q4
6 marks Moderate -0.8
In a triangle \(ABC\), \(AB = 5\sqrt{2}\) cm, \(BC = 8\) cm and angle \(B = 60°\).
  1. Find the exact area of the triangle, giving your answer as simply as possible. [3]
  2. Find the length of \(AC\), correct to 3 significant figures. [3]
AQA AS Paper 1 2024 June Q7
5 marks Moderate -0.8
A triangular field of grass, \(ABC\), has boundaries with lengths as follows: $$AB = 234 \text{ m} \qquad BC = 225 \text{ m} \qquad AC = 310 \text{ m}$$ The field is shown in the diagram below. \includegraphics{figure_7}
  1. Find angle \(A\) [2 marks]
  2. Farmers calculate the number of sheep they can keep in a field, by allowing one sheep for every \(1200 \text{ m}^2\) of grass. Find the maximum number of sheep which can be kept in the field \(ABC\) [3 marks]