3.2 Trigonometry in trianglesIB Maths: Applications and Interpretation SL: Subtopic test

1. 1
   A wheelchair ramp is a straight slope of length 6 m that rises 0.9 m to a platform. The ground is horizontal.

   (a)

   Find the angle the ramp makes with the horizontal ground.

   [1 mark]

   • A$8.63^\circ$
   • B$8.53^\circ$
   • C$81.4^\circ$
   • D$0.151^\circ$

   (b)

   Find the horizontal distance covered by the ramp.

   [1 mark]

   • A$6.07$ m
   • B$5.10$ m
   • C$5.93$ m
   • D$5.40$ m

   (c)

   A second ramp rises the same 0.9 m but is inclined at exactly $3^\circ$ to the horizontal. Find its length.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two observers $P$ and $Q$ stand 120 m apart on level ground. A drone $D$ hovers in the vertical plane through $P$ and $Q$, with $D\hat{P}Q=62^\circ$ and $D\hat{Q}P=48^\circ$.

   (a)

   Find the size of angle $P\hat{D}Q$.

   [1 mark]

   • A$110^\circ$
   • B$70^\circ$
   • C$14^\circ$
   • D$118^\circ$

   (b)

   Find the distance $PD$.

   [1 mark]

   • A$101$ m
   • B$113$ m
   • C$152$ m
   • D$94.9$ m

   (c)

   Find the distance $QD$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two hikers leave a hut $H$ along straight paths that meet at an angle of $115^\circ$. After some time, hiker $A$ is 3.5 km from $H$ and hiker $B$ is 5 km from $H$.

   (a)

   Find the distance between the two hikers.

   [3 marks]

   (b)

   (i) Find the size of angle $H\hat{B}A$.
   (ii) Find the area of triangle $HAB$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A field $ABCD$ is a quadrilateral with $AB=65$ m, $BC=50$ m, $CD=55$ m and $DA=40$ m. The angle $A\hat{B}C=70^\circ$. A calculator may be used.

   (a)

   (i) Find the length of $AC$.
   (ii) Find the size of angle $A\hat{D}C$.

   [6 marks]

   (b)

   (i) Find the area of triangle $ABC$.
   (ii) Find the area of triangle $ACD$.
   (iii) Grass seed for the whole field costs 3.40 AED per square metre. Find the total cost, to 3 significant figures.

   [6 marks]

   Total for question 4: 12 marks

End of questions