Cambridge International Mathematics

Trigonometry (Chapter 15) 317

FINDING TRIGONOMETRIC RATIOS

Example 3 Self Tutor

For the given triangle find

sinμ,cosμandtanμ:

sinμ=

OPP

HYP

=^45

cosμ=

ADJ

HYP

=^35

tanμ=

OPP

ADJ

=^43

FINDING SIDES

In a right angled triangle, if we are given another angle and a side we can find:

² the third angle using the ‘angle sum of a triangle is 180 o’

² the other sides using trigonometry.

Step 1: Redraw the figure and mark on it HYP, OPP, ADJ relative to the given angle.

Step 2: Choose the correct trigonometric ratio and use it to set up an equation.

Step 3: Solve to find the unknown.

Example 4 Self Tutor

Find the unknown length in the following triangles:

ab

a Now sin 61o=

x

9 : 6

fsinμ=

OPP

HYP

g

) sin 61o£ 9 :6=x f£both sides by 9 : 6 g

) x¼ 8 : 40 fSIN 61 ) £ 9 : 6 ENTERg

The length of the side is about 8 : 40 cm.

b Now tan 41o=

7 : 8

x

ftanμ=

OPP

ADJ

g

) x£tan 41o=7: 8 f£both sides byxg

) x=

7 : 8

tan 41o

f¥both sides by tan 41og

) x¼ 8 : 97 f 7 : 8 ¥ TAN 41 ) ENTERg

The length of the side is about 8 : 97 m.

3cm

4cm

5cm

q

q

OPP

HYP ADJ

xcm

61° 9.6 cm

HYP

OPP

ADJ

xcm

61° 9.6 cm

7.8 m xm

41°

HYP

OPP ADJ

7.8 m xm

41°

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Y:\HAESE\IGCSE01\IG01_15\317IGCSE01_15.CDR Friday, 26 September 2008 2:41:28 PM PETER