This document provides an introduction to trigonometric ratios and their uses in solving problems involving right triangles. It defines the trig functions of sine, cosine, and tangent and relates them to angle measurements and the sides of a right triangle. Examples are given for calculating trig ratios and using them to find missing side lengths or angle measures. The document also distinguishes between angles of elevation and depression and provides examples of applying trigonometry to problems involving these angle types.

1. Trig 1 May 09, 2011
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 hypotenuse
opposite adjacent
side side
adjacent opposite
side 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. Trig 1 May 09, 2011
Trig Ratios:
(where α represents the measure
of the perspective angle)
opposite side adjacent side opposite side
sin α = cos α = tan α =
hypotenuse hypotenuse adjacent side
Find each trigonometric ratio accurate to 4 decimal places:
sin 28o cos 65o tan 50o
Solve for x. Round to the nearest hundredth.
x
sin 50o =
x tan 33o =
20 26
20 38
cos 82o = tan 17o =
x x
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3. Trig 1 May 09, 2011
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
18.6
37o
n
m
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4. Trig 1 May 09, 2011
9
y
o
x
4
x
o
y
17
26
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5. Trig 1 May 09, 2011
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. Trig 1 May 09, 2011
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. Trig 1 May 09, 2011
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