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

Use Pythagoras and triangle sine/cosine/tangent methods to determine an unknown length or angle from a labelled real-world diagram.
Solve angle-of-elevation or angle-of-depression problems, constructing the diagram and identifying the correct horizontal, vertical and line-of-sight quantities.
Use bearings and non-right triangle rules to determine a direction, distance, area or meeting point, keeping the clockwise reference and units consistent.
Translate a multi-step distance, height, area, travel-time or cost model into connected triangle calculations and interpret the final value in context.

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Study SL 3.3—Applications of trigonometry conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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