Transcript Basic Trigonometry

Basic Trigonometry
Sine
Cosine
Tangent
The Language of Trig
The target
angle is either
one of the
acute angles
of the right
triangle.
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Trig Equations
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Trig Equations
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Trig Equations
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Given sides, find requested ratios:
• Locate indicated
angle and classify
sides in relation to it.
• Use proper equation
and write the ratio.
• Use calculator to
round to the nearest
ten-thousandths
place.
Find sin, cos, and tan of A.
8.2
24.5
23.1
24.5
8.2
23.1
Solving for the unknown:
• Unknown on top…..Multiply
x
24
Calculator: 24 * (sin 40)= 15.4
Solving for the unknown:
• Unknown on bottom…..Divide
24
x
Calculator: 24 (sin 40)= 37.3
Solving for the unknown:
• Unknown angle…..use inverse
x
15.4
24
Calculator: 2nd sin-1 (15.4/24)= 40
Solving problems using trig:
• Choose your target
angle and classify sides
in relation to it.
• Use proper equation
and write the ratio
placing the unknown
wherever it falls.
• Solve…Unless directed
otherwise, round sides
to nearest tenth and
angles to nearest
degree.
h
52.6
h = 52.6(sin 30) = 26.3
Angle of Elevation
The angle of
elevation is always
Measured from the
Horizontal UP…
It is always INSIDE
the triangle.
Angle of Depression
The angle of depression
is always
Measured from the
Horizontal DOWN…
It is usually OUTSIDE
the triangle.
x 
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However….because horizontal lines
are parallel, an angle of depression
is equal to its alternate interior
angle of elevation.
Practice
h
h
30m
67
30m
h = 30(tan 67) = 70.7m
From a point on the ground 25 feet from the foot
of a tree, the angle of elevation of the top of the
tree is 32º. Find to the nearest foot, the height of
the tree.
Adj
Hyp
Opp
x ft
32°
25 ft
x  16 ft