IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Trigonometry–Trigonometric ratios in right angled triangles
Topic :Trigonometry- Weightage : 21 %
All Questions for Topic : Triangle properties,Bearings,Pythagoras’ theorem,Trigonometric ratios in right angled triangles
Question (15 marks)
The following video explains the use of sleeves for paper cups.Cardboard sleeves are used to reduce the discomfort of holding a hot paper cup.the sleeve forms part of a sector of a circle as shown.In this question, you will make calculations to find the area of the sleeve
The dimensions of the sleeve are provided on the diagram, in centimetres $(\mathrm{cm})$.
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Question (a) : 3 marks
Show that the value of angle $y$ is $70^{\circ}$, to the nearest degree.
▶️Answer/Explanation
Ans:
The expression \(12.55 – 10.6\) can be simplified as follows:
\[12.55 – 10.6 = 1.95\]
So, \(12.55 – 10.6 = 1.95\).
The equation \(\cos y = \frac{1.95}{5.7}\) implies that the cosine of angle \(y\) is equal to \(\frac{1.95}{5.7}\).
To find the value of \(y\), we can take the inverse cosine (arccos) of \(\frac{1.95}{5.7}\):
\[y = \cos^{-1} \left(\frac{1.95}{5.7}\right)\]
Therefore, \(y = \cos^{-1} \left(\frac{1.95}{5.7}\right)\Rightarrow 70^{\circ}\).
Question (b) : 2 marks
Hence, determine the value of angle $x$, to the nearest degree.
▶️Answer/Explanation
Ans:
\( \begin{gathered}90^{\circ}-70^{\circ}=\frac{x }{ 2} \\ x=40^{\circ}\end{gathered} \)