IB Maths AA SL 3.3 Applications of Trigonometry Questions

Practise solving applied triangle problems with Pythagoras, trigonometry, bearings and elevation angles, translating multi-step models into units-based conclusions.

Exam points

Apply Pythagoras and right or non-right triangle trigonometry to determine unknown lengths or angles from a labelled diagram.
Solve elevation, depression and bearing problems by constructing a correctly oriented diagram, identifying the reference direction and interpreting the resulting triangle.

[Maximum number: 3]

A monument is in the shape of a right cone with a vertical height of 20 metres. Oliver stands 5 metres from the base of the monument. His eye level is 1.8 metres above the ground and the angle of elevation from Oliver's eye level to the vertex of the cone is $58^{\circ}$ , as shown on the following diagram.

Figure for Question IB Maths AA SL 3.3 Applications of Trigonometry Questions question 1 — IB Maths AA SL

Find the radius of the base of the cone.

attempt to use trigonometry to find the radius of the cone OR Oliver's distance from
centre (r+5)

\begin{aligned} & \tan 58^{\circ}=\frac{18.2}{r+5} \text { OR } \frac{r+5}{\sin 32^{\circ}}=\frac{18.2}{\sin 58^{\circ}} \text { OR }(r+5=) 11.3726 \ldots \\ & r=6.37262 \ldots(\mathrm{~m}) \\ & (r=) 6.37(\mathrm{~m}) \end{aligned}

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IB Maths AA SL 3.3 Applications of Trigonometry Questions question 1