Trigonometric Ratios Worksheet Page 16
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22Example
Determine the length of f to one decimal place.
D
19.5 m
f
F
118°
12.6 m
E
Solution
Two side lengths and one angle measure are given. Check for the ambiguous case.
Side e is opposite the known angle.
Since e > d, only one triangle is possible.
Determine ∠D.
sin D
sin E
_____
_____
=
e
d
sin D
sin 118°
_____
_______
=
12.6
19.5
12.6 sin 118°
___________
sin D =
19.5
(
)
12.6 sin 118°
___________
∠ D = sin
–1
19.5
= 34.7864…°
� � 34.8°
34.8°
Determine ∠F.
∠F = 180° − (118° + 34.8°)
= 27.2°
Determine f.
f
e
_____
_____
=
sin F
sin E
f
19.5
________
_______
=
sin 27.2°
sin 118°
19.5 sin 27.2°
___________
f =
sin 118°
= 10.0950…
� 10.1
The length of side f is approximately 10.1 m.
16 MHR • Chapter 1 978-0-07-090893-2
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