This document discusses trigonometric ratios and their use in right triangles. It defines the three basic trig functions - sine, cosine, and tangent - which relate angles to sides of a right triangle. Sine is defined as the ratio of the opposite side to the hypotenuse. Cosine is the ratio of the adjacent side to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. Several examples are given of calculating trig ratios and solving for unknown sides or angles in right triangles. Angles of elevation and depression are also defined.

1. SOHCAHTOA
Trigonometric Ratios
Objectives:
1. To find trigonometric ratios using right triangles.
2. Solve problems using trigonometric ratios.
What is trigonometry?
Trigonometry is the study of the relationships between the sides & the angles of
Δ.
The key to basic trigonometry to is determine which sides are involved when
looking from the angle of perspective.
Angle of Perspective : the angle from which you are looking
hypotenuse
opposite
side
hypotenuse
adjacent
side
opposite
side
adjacent
side
There are 3 basic trigonometric functions:
sine (sin) cosine (cos)
tangent (tan)
These trigonometric ratios are related to angle measurements.
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2. SOHCAHTOA
Trig Ratios:
(where α represents the measure
of the perspective angle)
sin α =
opposite side
cos α =
hypotenuse
adjacent side
tan α =
hypotenuse
opposite side
adjacent side
Find each trigonometric ratio accurate to 4 decimal places:
sin 28o
cos 65 o
tan 50 o
Solve for x. Round to the nearest hundredth.
x
tan 33 o =
sin 50o =
20
cos 82 o =
20
x
tan 17 o =
x
26
38
x
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3. SOHCAHTOA
Find the measure of each angle to the nearest degree.
sin α =.471
cos δ = 1
tan θ = 1.57
Find the measure of the missing information accurate to the nearest whole unit.
22
x
25o
y
37o
18.6
n
m
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4. SOHCAHTOA
9
y
xo
4
x
o
y
26
17
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5. SOHCAHTOA
Angles of Elevation
An angle of elevation is the angle between the line of
sight and the horizontal when an observer looks upward.
Angles of Depression
An angle of depression
is the angle between the line of sight when an
observer looks downward, and the horizontal.
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6. SOHCAHTOA
An airplane is flying at a height of 2 miles above the ground. The
distance along the ground from the airplane to the airport is 5 miles.
What is the angle of depression from the airplane to the airport?
A building is 50 feet high. At a distance away from the building, an observer
notices that the angle of elevation to the top of the building is 41º. How far is the
observer from the base of the building?
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7. SOHCAHTOA
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