IB Maths AA SL AA 3.1 3D geometry and triangle 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.

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Question 1

Paper 2, calculatorEasy5 marks

During map-making, a survey team records three landmarks, $P$ $A$ and $B$ The distances $PA$ and $PB$ are $8.0\text{ km}$ and $11.0\text{ km}$ respectively, and $\angle APB=60.0^\circ$

Give your answers to three significant figures.

(a)

Using the cosine rule, determine the distance $AB$

[3]

(b)

Calculate the area of triangle $PAB$

[2]

A square-based right pyramid models a roof structure. The side length of its horizontal base is $4\text{ m}$ The apex $S$ is vertically above the centre $O$ of the base, and $SO=2\sqrt{2}\text{ m}$ Let $A$ be a vertex of the base.

(a)

Determine the distance $OA$

[2]

(b)

Hence determine the distance $SA$

[2]

(c)

Determine the angle between $SA$ and the plane of the base. Give your answer in degrees.

[2]

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