Transcript Applying trigonometry

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The three trigonometric ratios
H
Y
P
O
T
E
N
U
S
E
O
P
P
O
S
I
T
E
Opposite
Sin θ =
Hypotenuse
SOH
Adjacent
Cos θ =
Hypotenuse
CAH
Opposite
Tan θ =
Adjacent
TOA
θ
ADJACENT
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Finding side lengths
If we are given one side and one acute angle in a right-angled
triangle, we can use one of the three trigonometric ratios to
find the lengths of other sides.
Find x to 2 decimal places.
To find the length of the side opposite
the angle, given the hypotenuse, use:
12 cm
56°
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x
opposite
sin θ =
hypotenuse
x
sin 56° =
12
x = 12 × sin 56°
= 9.95 cm
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Finding side lengths
A 5 m ladder is resting against a wall. It makes an angle of
70° with the ground.
What is the distance between the
base of the ladder and the wall?
To find the length of the side adjacent
to the angle, given the hypotenuse, use:
5m
70°
x
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adjacent
cos θ =
hypotenuse
x
cos 70° =
5
x = 5 × cos 70°
= 1.71 m (to 2 d.p.)
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Finding angles
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