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Lesson Objectives
• SWKOL how to use trigonometry to obtain
values of sides and angles of right triangles
Trigonometry
• Trigonometry relates the various sides and
angles of right triangles
• It is important to remember that all triangles
have angles totaling 180°
• Because a right triangle always has an angle
of 90°, the other two angles must add up to
90° also
Angle Examples
• What is the missing angle theta (q)?
56°
q
34°
Angle Examples
• What is the missing angle theta (q)?
72°
q
18°
Trigonometry
• Three functions in trigonometry relate the
angles of a right triangle to its sides: sine,
cosine, and tangent
• By knowing how to use these functions, you
can determine the value of any side of a
right triangle when given the value of one
side and angle
Trigonometry
• There are three anagrams to remember the
trigonometric functions
• SOH: Sin(q) = opposite/hypotenuse
• CAH: Cos(q) = adjacent/hypotenuse
• TOA: Tan(q) = opposite/adjacent
Trigonometry
• The hypotenuse is the side opposite to the
right angle
• The opposite side is the side opposite to the
angle theta (q)
• The adjacent side is the side next to the
angle theta (q) that is not the hypotenuse
Sides of a right triangle
hypotenuse
opposite
90o
Θ
adjacent
Side Examples
• Use the trigonometric functions in your
calculator to solve for the side X
60°
15
90o
X
sin(60°) = 0.866 = x/15; x = 13
Side Examples
• Use the trigonometric functions in your
calculator to solve for the side X
45°
7.3
X
90o
cos(45°) = 0.7071 = x/7.3; x = 5.2
Side Examples
• Use the trigonometric functions in your
calculator to solve for the side X
53.7
90o
30°
X
tan(30°) = 0.5774 = 53.7/x; x = 93.0
Trigonometry
• You can also solve for the angles of a right
triangle by using the same equations if you
are given two of the sides
Angle Examples
• Use the trigonometric functions in your
calculator to solve for the angle q
64.4
q
32.2
90o
cos(q) = 32.2/64.4 = 0.500; q = 60°
Angle Examples
• Use the trigonometric functions in your
calculator to solve for the angle q
q
5.0
8.7
tan(q) = 8.7/5.0 = 1.7; q = 60°
Angle Examples
• Use the trigonometric functions in your
calculator to solve for the angle q
17.5
12.4
q
sin(q) = 12.4/17.5 = 0.709; q = 45°
Side Examples
• Use the trigonometric functions in your calculator to
solve for the sides x and y
17.0
y
40o
x= 17.0*cos40o =13.0
x
y=17.0*sin40o=10.9
Trigonometry
• The concepts that we discussed in this
lesson will be important when we work with
vectors.