Edexcel IGCSE Math B 9.C Elevation & depression Question Bank

Practise modelling angles of elevation and depression with horizontal ground, vertical objects and right-triangle trigonometry.

Exam points

convert horizontal distances and heights into a right triangle, then use tan to find a pole or building height
interpret depression angles as equal alternate angles before calculating a distance or angle
account for height differences between vertical objects before applying trigonometry

[Maximum number: 3]

Figure for Question 9.C Elevation and depression question 1 — Edexcel IGCSE Math B

Figure 3 shows a solid right prism ABCDEFGH.
Diagram NOT accurately drawn.
The base of the prism, ABCD, is a rectangle and is horizontal. Trapezium BCHG is a cross section of the prism.
$AB=4\text{ m},\quad BC=3\text{ m},\quad CH=2.4\text{ m},\quad GB=1.5\text{ m}$ $\angle GBC=\angle BCH=\angle ABG=\angle DCH=90^\circ$

Calculate the angle of depression, in degrees to one decimal place, of G from E.

Horizontal diagonal:
$DB=\sqrt{4^{2}+3^{2}}=5$
Vertical difference:
2.4-1.5=0.9 $\tan\theta=\frac{0.9}{5}$
Final answer:
$10.2^\circ$
An answer of $79.8^\circ$ gains 2 marks.

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9.C Elevation and depression question 1