1.05c Area of triangle: using 1/2 ab sin(C)

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WJEC Unit 1 2024 June Q5
4 marks Moderate -0.5
A triangle \(ABC\) has sides \(AB = 6\)cm, \(BC = 11\)cm and \(AC = 13\)cm. Calculate the area of the triangle. [4]
WJEC Unit 1 Specimen Q5
12 marks Moderate -0.8
The points \(A(0, 2)\), \(B(-2, 8)\), \(C(20, 12)\) are the vertices of the triangle \(ABC\). The point \(D\) is the mid-point of \(AB\).
  1. Show that \(CD\) is perpendicular to \(AB\). [6]
  2. Find the exact value of \(\tan CAB\). [5]
  3. Write down the geometrical name for the triangle \(ABC\). [1]
WJEC Unit 1 Specimen Q8
6 marks Moderate -0.3
The circle \(C\) has radius 5 and its centre is the origin. The point \(T\) has coordinates \((11, 0)\). The tangents from \(T\) to the circle \(C\) touch \(C\) at the points \(R\) and \(S\).
  1. Write down the geometrical name for the quadrilateral \(ORTS\). [1]
  2. Find the exact value of the area of the quadrilateral \(ORTS\). Give your answer in its simplest form. [5]
SPS SPS SM 2020 June Q2
9 marks Moderate -0.3
\includegraphics{figure_1} Figure 1 shows the plan view of a design for a stage at a concert. The stage is modelled as a sector \(BCDF\), of a circle centre \(F\), joined to two congruent triangles \(ABF\) and \(EDF\). Given that - \(AFE\) is a straight line - \(AF = FE = 10.7\)m - \(BF = FD = 9.2\)m - angle \(BFD = 1.82\) radians find
  1. the perimeter of the stage, in metres, to one decimal place, [5]
  2. the area of the stage, in m², to one decimal place. [4]
SPS SPS FM 2020 October Q5
6 marks Moderate -0.3
\includegraphics{figure_5} The diagram shows triangle \(ABC\), with \(AB = x\) cm, \(AC = (x + 2)\) cm, \(BC = 2\sqrt{7}\) cm and angle \(CAB = 60°\).
  1. Find the value of \(x\). [4]
  2. Find the area of triangle \(ABC\), giving your answer in an exact form as simply as possible. [2]
SPS SPS FM 2025 October Q2
6 marks Moderate -0.8
In a triangle \(ABC\), \(AB = 9\) cm, \(BC = 7\) cm and \(AC = 4\) cm.
  1. Show that \(\cos CAB = \frac{2}{3}\). [2]
  2. Hence find the exact value of \(\sin CAB\). [2]
  3. Find the exact area of triangle \(ABC\). [2]
OCR H240/03 2017 Specimen Q8
6 marks Standard +0.8
In this question you must show detailed reasoning. The diagram shows triangle \(ABC\). \includegraphics{figure_8} The angles \(CAB\) and \(ABC\) are each \(45°\), and angle \(ACB = 90°\). The points \(D\) and \(E\) lie on \(AC\) and \(AB\) respectively. \(AE = DE = 1\), \(DB = 2\). Angle \(BED = 90°\), angle \(EBD = 30°\) and angle \(DBC = 15°\).
  1. Show that \(BC = \frac{\sqrt{2} + \sqrt{6}}{2}\). [3]
  2. By considering triangle \(BCD\), show that \(\sin 15° = \frac{\sqrt{6} - \sqrt{2}}{4}\). [3]