CAIE IGCSE Mathematics Extended E6.2.2 Solve Problems in Two Dimensions Using Pythagoras Theorem and Questions

Practise Extended CAIE IGCSE Mathematics by identifying right triangles in diagrams and calculating missing distances.

Exam points

Solve two-dimensional problems using Pythagoras’ theorem in composite diagrams.
Identify right-angled triangles and calculate missing lengths or distances.
Combine Pythagoras’ theorem with geometric or coordinate information in context.

[Maximum number: 6]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

NOT TO
SCALE

The diagram shows a right-angled triangle PQR on horizontal ground. X is vertically above R and the angle of elevation of X from P is $21^{\circ}$ . $X R=2.8 \mathrm{~m}$ and $R Q=7.1 \mathrm{~m}$ .

[ 3 ]

(i)

Calculate PQ.

[ 3 ]

10.2 or 10.17 to 10.18
M2 for $\left(\frac{2.8}{\tan21}\right)^2+7.1^2$ oe
or M1 for $\frac{2.8}{PR}=\tan21$ oe

(b)

Figure for Question (b) — CAIE IGCSE Mathematics Extended

The area of triangle ABC is $62.89 \mathrm{~cm}^{2}$ .

[ 3 ]

(i)

AB is extended to a point D such that angle B D C=90^.

Calculate BD.
cm

[ 3 ]

6.6[0] to 6.62
M2 for $21.5\cos28.4-12.3$
or M1 for $21.5\cos28.4$

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CAIE IGCSE Mathematics Extended E6.2.2 Solve Problems in Two Dimensions Using Pythagoras Theorem and Questions question 1

Question (a)

Question (i)

Question (b)

Question (i)