Area of a triangle using sineIB MYP Maths Extended: Subtopic test

1. 1
   In triangle $ABC$, $AB=10$ cm, $BC=14$ cm and $A\hat BC=30^\circ$.

   (a)

   Find the area of triangle $ABC$.

   [1 mark]

   • A$70$ cm$^2$
   • B$35$ cm$^2$
   • C$60.6$ cm$^2$
   • D$140$ cm$^2$

   (b)

   Find the length of $AC$.

   [1 mark]

   • A$23.2$ cm
   • B$17.2$ cm
   • C$53.5$ cm
   • D$7.32$ cm

   (c)

   Find the shortest distance from $A$ to the line $BC$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   $PQRS$ is a parallelogram with $PQ=12$ cm, $QR=9$ cm and $P\hat QR=70^\circ$.

   (a)

   Find the area of triangle $PQR$.

   [1 mark]

   • A$50.7$ cm$^2$
   • B$18.5$ cm$^2$
   • C$54$ cm$^2$
   • D$101.5$ cm$^2$

   (b)

   Find the area of the parallelogram $PQRS$.

   [1 mark]

   • A$50.7$ cm$^2$
   • B$54$ cm$^2$
   • C$101.5$ cm$^2$
   • D$108$ cm$^2$

   (c)

   Find the length of the diagonal $PR$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A ship leaves port $A$ and sails 8 km on a bearing of $040^\circ$ to a buoy $B$. It then sails 6 km on a bearing of $100^\circ$ to a second buoy $C$.

   (a)

   Find the angle $A\hat BC$.

   [3 marks]

   (b)

   Find the area of triangle $ABC$ and the distance $AC$ between the port and the second buoy.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A triangular shade sail for a school playground has two edges, of lengths 10 m and 12 m, that meet at a corner post at an angle $\theta$.

   (a)

   Find the area of the sail when $\theta=30^\circ$, $60^\circ$, $90^\circ$ and $150^\circ$.
   Describe how the area changes as $\theta$ increases from $0^\circ$ to $180^\circ$, and explain why $30^\circ$ and $150^\circ$ give the same area.

   [6 marks]

   (b)

   The sail must give at least 45 m$^2$ of shade, and the third edge, joining the ends of the two given edges, must be no longer than 17 m so that it fits between the anchor points. A designer proposes $\theta=110^\circ$.
   (i) Evaluate whether this proposal meets both conditions.
   (ii) Suggest a different value of $\theta$ that meets both conditions, and show that it does.

   [6 marks]

   Total for question 4: 12 marks

End of questions