Transcript Applying trigonometry

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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 angles
8 cm
Find θ to 2 decimal places.
5 cm
θ
We are given the lengths of the sides opposite and adjacent
to the angle, so we use:
opposite
tan θ =
adjacent
8
tan θ =
5
θ = tan–1 (8 ÷ 5)
= 57.99° (to 2 d.p.)
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Finding angles and lengths
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Angles of depression
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The inverse of sin
sin θ = 0.5, what is the value of θ?
To work this out use the sin–1 key on the calculator.
sin–1 0.5 = 30°
sin–1 is the inverse of sin. It is sometimes called arcsin.
sin
30°
0.5
sin–1
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The inverse of cos
cos θ = 0.5, what is the value of θ?
To work this out use the cos–1 key on the calculator.
cos–1 0.5 = 60°
cos–1 is the inverse of cos. It is sometimes called arccos.
cos
60°
0.5
cos–1
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The inverse of tan
tan θ = 1, what is the value of θ?
To work this out use the tan–1 key on the calculator.
tan–1 1 = 45°
tan–1 is the inverse of tan. It is sometimes called arctan.
tan
45°
1
tan–1
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