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IB Maths AA HL 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.

Syllabus
First assessment 2021
Course
Mathematics: analysis and approaches HL
Level
HL

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.

Learn this topic

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

IB Maths AA HL Sl 3 3 Applications of Trigonometry Questions question 1

[Maximum number: 5]

The following question compares the distance and direction between cities on a flat surface to the distance and direction between cities on a sphere.
Consider a model where the cities of Bogotá, Moscow, and Nairobi lie on a flat surface. In this model, Nairobi is 6000 km due south of Moscow and Bogotá is 12500 km due west of Nairobi, as shown in the following diagram.

Figure for Question IB Maths AA HL Sl 3 3 Applications of Trigonometry Questions question 1 — IB Maths AA HL

Question (a)

(a)

Find the distance from Bogotá to Moscow.

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Question (b)

(b)

Find the bearing of Moscow from Bogotá. Give your answer in degrees.

In reality, these three cities lie on the curved surface of the Earth which will change the distances and directions found in part (a).

Now consider a curved model using a coordinate system (x, y, z) with its origin, O , at the centre of the Earth. The units of this system are thousands of kilometres and the Earth is modelled as a sphere with radius 6000 km . The North Pole, P, lies on the z-axis, and Nairobi, N, is modelled as being on the equator and lying on the y-axis.

Figure for Question (b) — IB Maths AA HL

P has position vector OP→=p=(006)\overrightarrow{\mathrm{OP}}=\boldsymbol{p}=\left(\begin{array}{l}0 \\ 0 \\ 6\end{array}\right) and N has position vector ON→=n=(060)\overrightarrow{\mathrm{ON}}=\boldsymbol{n}=\left(\begin{array}{l}0 \\ 6 \\ 0\end{array}\right).

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