Real-world application problems

A question is this type if and only if it involves a practical context (gardens, buildings, fields, etc.) requiring interpretation and modelling before applying sine or cosine rules.

5 questions · Moderate -0.1

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 P1 2019 January Q7
6 marks Moderate -0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c8f8d35d-c2dd-4a1f-a4bb-a4fa06413d12-14_327_595_251_676} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Not to scale Figure 3 shows the design for a structure used to support a roof. The structure consists of four wooden beams, \(A B , B D , B C\) and \(A D\). Given \(A B = 6.5 \mathrm {~m} , B C = B D = 4.7 \mathrm {~m}\) and angle \(B A C = 35 ^ { \circ }\)
  1. find, to one decimal place, the size of angle \(A C B\),
  2. find, to the nearest metre, the total length of wood required to make this structure.
OCR MEI C2 2007 January Q11
12 marks Standard +0.3
11 Fig. 11.1 shows a village green which is bordered by 3 straight roads \(A B , B C\) and \(C A\). The road AC runs due North and the measurements shown are in metres. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b4c0b4b0-f13c-49a9-9f98-f86f28d1f577-4_460_1143_486_591} \captionsetup{labelformat=empty} \caption{Fig. 11.1}
\end{figure}
  1. Calculate the bearing of B from C , giving your answer to the nearest \(0.1 ^ { \circ }\).
  2. Calculate the area of the village green. The road AB is replaced by a new road, as shown in Fig. 11.2. The village green is extended up to the new road. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{b4c0b4b0-f13c-49a9-9f98-f86f28d1f577-4_440_1002_1436_737} \captionsetup{labelformat=empty} \caption{Fig. 11.2}
    \end{figure} The new road is an arc of a circle with centre O and radius 130 m .
  3. (A) Show that angle AOB is 1.63 radians, correct to 3 significant figures.
    (B) Show that the area of land added to the village green is \(5300 \mathrm {~m} ^ { 2 }\) correct to 2 significant figures.
Edexcel AS Paper 1 2020 June Q5
6 marks Standard +0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bcbd842f-b2e2-4587-ab4c-15a57a449e5d-10_360_1164_260_607} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the design for a structure used to support a roof.
The structure consists of four steel beams, \(A B , B D , B C\) and \(A D\).
Given \(A B = 12 \mathrm {~m} , B C = B D = 7 \mathrm {~m}\) and angle \(B A C = 27 ^ { \circ }\)
  1. find, to one decimal place, the size of angle \(A C B\). The steel beams can only be bought in whole metre lengths.
  2. Find the minimum length of steel that needs to be bought to make the complete structure.
AQA AS Paper 2 2019 June Q5
4 marks Moderate -0.3
5 A triangular prism has a cross section \(A B C\) as shown in the diagram below. Angle \(A B C = 25 ^ { \circ }\) Angle \(A C B = 30 ^ { \circ }\) \(B C = 40\) millimetres. The length of the prism is 300 millimetres.
Calculate the volume of the prism, giving your answer to three significant figures.
Edexcel AS Paper 1 Specimen Q8
5 marks Moderate -0.3
\includegraphics{figure_1} A triangular lawn is modelled by the triangle \(ABC\), shown in Figure 1. The length \(AB\) is to be \(30\text{m}\) long. Given that angle \(BAC = 70°\) and angle \(ABC = 60°\),
  1. calculate the area of the lawn to \(3\) significant figures. [4]
  2. Why is your answer unlikely to be accurate to the nearest square metre? [1]