Sine and cosine rules and area of a triangleEdexcel International A Level Maths: Subtopic test

1. 1
   In triangle $PQR$, $PQ=12$ cm, $PR=9$ cm and angle $QPR=40^{\circ}$.

   (a)

   Find the length of $QR$.

   [1 mark]

   • A$15.0$ cm
   • B$19.8$ cm
   • C$59.5$ cm
   • D$7.72$ cm

   (b)

   Find the area of triangle $PQR$.

   [1 mark]

   • A$69.4$ cm$^2$
   • B$41.4$ cm$^2$
   • C$34.7$ cm$^2$
   • D$54.0$ cm$^2$

   (c)

   Find the size of angle $PQR$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A triangular plot of land $ABC$ has $AB=140$ m, $AC=95$ m and $BC=180$ m.

   (a)

   Find the size of angle $BAC$.

   [1 mark]

   • A$81.8^{\circ}$
   • B$98.2^{\circ}$
   • C$106.5^{\circ}$
   • D$50.3^{\circ}$

   (b)

   Find the area of the plot.

   [1 mark]

   • A$6580$ m$^2$
   • B$3290$ m$^2$
   • C$13\,200$ m$^2$
   • D$944$ m$^2$

   (c)

   Find the size of the smallest angle of the plot.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In triangle $ABC$, $AB=8.4$ cm, angle $ABC=52^{\circ}$ and angle $ACB=71^{\circ}$.

   (a)

   Find the length of $AC$.

   [3 marks]

   (b)

   Find the length of $BC$ and hence the area of triangle $ABC$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In triangle $ABC$, $AB=12$ cm, $BC=8$ cm and angle $BAC=35^{\circ}$.

   (a)

   (i) Use the sine rule to find the two possible sizes of angle $ACB$.
   (ii) Show that both values give a valid triangle.

   [6 marks]

   (b)

   Find the area of each of the two possible triangles.

   [6 marks]

   Total for question 4: 12 marks

End of questions