Cambridge International Mathematics

Trigonometry (Chapter 15) 323

ANGLES OF ELEVATION AND DEPRESSION

The angle between the horizontal and your line of sight

is called theangle of elevation if you are looking

upwards, or theangle of depressionif you are looking

downwards.

If the angle of elevation from A to B isμo, then the

angle of depression from B to A is alsoμo.

When using trigonometry to solve problems we often use:

² the properties of isosceles and right angled triangles

² the properties of circles and tangents

² angles of elevation and depression.

Example 6 Self Tutor

cosμ=

ADJ

HYP

) cos 16o=

x

9 : 4

) x=9: 4 £cos 16o

) x¼ 9 : 036

fCalculator: 9 : 4 £ COS 16 ) ENTERg

) the length of the beam=2£ 9 : 036 m

¼ 18 : 1 m

Example 7 Self Tutor

A ladder 4 : 1 m in length rests against a vertical wall and reaches

3 : 5 m up from ground level. Find:

a the angle the ladder makes with the ground

b the distance from the foot of the ladder to the wall using

trigonometry.

angle of elevation

angle of depression

horizontal

observer

object

object

A

B

q°

q°

3.5 m

4.1 m

16°

9.4 m

beam

Determine the length of the horizontal

roofing beam required to support a roof

of pitch 16 oas shown alongside:

16°

9.4 m

xm xm

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Y:\HAESE\IGCSE01\IG01_15\323IGCSE01_15.CDR Friday, 26 September 2008 3:51:32 PM PETER