Cambridge International Mathematics

324 Trigonometry (Chapter 15)

a sinμ=

OPP

HYP

=

3 : 5

4 : 1

) μ= sin¡^1

μ

3 : 5

4 : 1

¶

) μ¼ 58 : 6 o

fSHIFT sin ( 3 : 5 ¥ 4 : 1 ) EXE g

) the ladder makes an angle of about

58 : 6 owith the ground.

b cosμ=

ADJ

HYP

) cos 58: 61 o=

x

4 : 1

) 4 : 1 £cos 58: 61 o=x

) 2 : 14 ¼x

) the foot of the ladder is about

2 : 14 m from the wall.

Example 8 Self Tutor

The angle between a tangent from point P to a circle and the line from P to the centre of the circle is

27 o. Determine the length of the line from P to the centre of the circle if the radius is 3 cm.

sinμ=

OPP

HYP

) sin 27o=

3

x

) x=

3

sin 27o

) x¼ 6 : 61

) CP has length approximately 6 : 61 cm.

EXERCISE 15C

1 From a point 235 m from the base of a cliff, the angle of elevation to the cliff top is 25 o. Find the

height of the cliff.

2 What angle will a 5 m ladder make with a wall if it reaches 4 : 2 m up the wall?

3 The angle of elevation from a fishing boat to the top of a lighthouse 25 m above sea-level is 6 o.

Calculate the horizontal distance from the boat to the lighthouse.

4

5

3.5 m

4.1 m

xm

q

27°

xcm

3cm

C

P

A rectangular gate has a diagonal strut of length m.

The angle between the diagonal and a side is. Find

the length of the longer side of the gate.

3

28 o

62°

Sam

A model helicopter takes off from the horizontal ground

with a constant vertical speed of 5 m/s. After 10 seconds

the angle of elevation from Sam to the helicopter is 62 o.

Sam is 1 : 8 m tall. How far is Sam’s head from the

helicopter at this time?

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