IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Trigonometry–Volume and capacity
Topic :Trigonometry- Weightage : 21 %
All Questions for Topic : Converse of Pythagoras’ theorem,Sine rule and cosine rule, including applications (link to trigonometric functions)
Question
The lines $B D$ and $C E$ pass through the centre $(O)$ of the circle.
$\bullet$ Determine the value of the angle DAC.
$\bullet$ Write down the value of the angle ADE.
$\bullet$ Determine the value of the angle AEC.
$\bullet$ Find the value of the angle OGD.
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▶️Answer/Explanation
Ans:
a (DAC =) 58 (degrees)
b (ADE =) 28
c 180 – (90 + 28) OR 90 – 28
(AEC =) 62
d (OED =) 58
• (OGD =) sum of their 58 OED and their 28 ADE
• Their = 86
Question (a)
An engineer is examining a weak bridge from a safe distance. In order to make a calculation for the height of the bridge to the ground vertically below she uses a measuring instrument called a theodolite that allows her to measure angles accurately. The theodolite is set at a height of 1.2 metres $(\mathrm{m})$. It is placed $57.25 \mathrm{~m}$, to the nearest centimetre, from the point $A$ at the bottom of the bridge. The angle of elevation from the horizontal to the top of the arch at $B$ is measured at $22^{\circ}$ to the nearest degree.
The measurements are modelled in the diagram below which is a side view from the bridge to the theodolite.
Calculate the height from the top of the bridge at $\rm B$ to the ground vertically below at $\rm A$ to the nearest centimetre.
▶️Answer/Explanation
Ans:
$\tan 22=\frac{\text { height }}{57.25}$
\[\tan 22 \times 57.25 = \text{height}\]
Using a calculator, we can find the value of \(\tan 22\) to be approximately 0.4040:
\[0.4040 \times 57.25 = \text{height}\]
Simplifying the calculation:
\[23.069 \approx \text{height}\]
Therefore, the height is approximately 23.069.
$\rm{AB}=23.069 + 1.2 = 24.269$