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

Solve two-dimensional Extended CAIE IGCSE Mathematics problems by linking right triangles, forming Pythagorean equations and using trigonometric ratios to find distances or angles.

Exam points

Form and solve a Pythagorean equation from algebraic side lengths, then use a trigonometric ratio to find the required acute angle.
Transfer a calculated side between adjoining right triangles, using exact trigonometric values when a surd answer is required.
Use a cosine projection and subtract the adjoining segment to find an extension beyond a triangle.
Resolve a bearing into perpendicular components, combine the east-west and north-south displacements, and use Pythagoras to find the direct distance.

[Maximum number: 2]

NOT TO SCALE

The diagram shows triangle ABC on horizontal ground.
$A C=15 \mathrm{~m}, B C=8 \mathrm{~m}$ and $A B=20 \mathrm{~m}$ .
BP and CQ are vertical poles of different heights.
$B P=3 \mathrm{~m}$ and $C Q=4 \mathrm{~m}$ .
AQ and PQ are straight wires.

Calculate the length of AQ.

15.5 or 15.52 to 15.53
M1 for $15^2+4^2$ oe

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