IB Maths AA HL Topic 3: Geometry and trigonometry questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1, no calculator Paper 2, calculator

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Question 1

Paper 1, no calculatorMedium6 marks

A survey team uses two points, $A$ and $B$ on level ground to locate the base $P$ of a vertical signal mast. Bearings are measured clockwise from north. Figure 1 is not to scale.

(a)

Use the plan view in Figure 1 to determine $AP$ Give your answer in exact form.

[4]

(b)

Hence, or otherwise, determine the height $PT$ of the mast. Give your answer in exact form.

[2]

Question 2

Paper 1, no calculatorMedium6 marks

In triangle $ABC$ the sides $a$ $b$ and $c$ are opposite the angles $A$ $B$ and $C$ respectively. Angles are measured in radians.

It is given that $A=\frac{\pi}{6}$ $a=6$ and $b=6\sqrt{3}$

(a)

Determine all possible values of $B$

[2]

(b)

Hence determine the corresponding values of $C$

[2]

(c)

For the obtuse value of $B$ determine the exact value of $\tan B$

[2]

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