This document discusses trigonometric ratios and their use in solving problems involving right triangles. It defines the three basic trigonometric functions - sine, cosine, and tangent - in terms of ratios of the sides of a right triangle with a given angle. Examples are provided to demonstrate calculating trigonometric ratios and using them to find missing side lengths or angle measures. The document also distinguishes between angles of elevation, which involve looking upward, and angles of depression, which involve looking downward. Sample word problems applying these angle concepts are presented at the end.

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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.
There are 3 basic trigonometric functions:
sine (sin) cosine (cos) tangent (tan)
These trigonometric ratios are related to angle measurements.
hypotenuse
adjacent
side
opposite
side
Angle of Perspective : the angle from which you are looking
hypotenuse
adjacent
side
opposite
side

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opposite side
hypotenuse
adjacent side
sin α =
Trig Ratios:
(where α represents the measure
of the perspective angle)
opposite side
hypotenuse
cos α =
adjacent side
tan α =
Find each trigonometric ratio accurate to 4 decimal places:
sin 28o cos 65o tan 50o
Solve for x. Round to the nearest hundredth.
sin 50o
=
x
20
tan 33o
=
x
26
cos 82o =
x
20
tan 17o =
x
38

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25o
x
22
Find the measure of the missing information accurate to the nearest whole unit.
Find the measure of each angle to the nearest degree.
sin α =.471 cos δ = 1 tan θ = 1.57
y
m
n
18.6
37o

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x
yo
17
26
4
9
xo
y

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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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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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