Transcript Trigonometry Basic Calculations of Angles and Sides of Right Triangles Determine an unknown angle • Given that C is a right angle, find A,

Trigonometry
Basic Calculations of Angles and
Sides of Right Triangles
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Determine an unknown angle
1
• Given that C is a right angle,
find A, B, and c.
a=8.5”
A
b=12.8”
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Determine an unknown angle
Example 1
• Let the unknown angle A be the reference
angle.
8.5”
A
12.8
”
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•
Determine
an
unknown
angle
Now label the sides of the right triangle...
Example 1
opposite
8.5”
hypotenuse
A
adjacent 12.8”
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Determine an unknown angle
Example 1
• Note that we only know the lengths of the
opposite and adjacent sides.
opposite
8.5”
hypotenuse
A
adjacent 12.8”
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Determine an unknown angle
Example 1
• So we need to pick a trig function that has
the opposite and adjacent sides in it...
opposite
8.5”
A
adjacent 12.8”
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Determine an unknown angle
Example 1
• Which trig function should you pick?
opp
sin A 
hyp
opposite
adj
cos A 
hyp
8.5”
A
12.8”
adjacent
opp
tan A 
adj
You need to pick the
tangent function since it
is the only one that has
both opposite and
adjacent sides in it.
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Determine an unknown angle
Example 1
• Now plug-in the numbers you have into the
tangent function...
opp
tan A 
adj
=8.5/12.8 = 0.8840625
A = 33.6°
opposite
8.5”
A
adjacent 12.8”
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Determine an unknown angle
Example 1
• How could you determine the size of the
remaining angle?
…this one must be 56.4° degrees.
(Since 180° - 90° - 33.6° = 56.4°)
56.4°
8.5”
..and this one
was computed
to be 33.6°…
This angle is
90°…
33.6°
12.8”
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Determine an unknown angle
Example 2
• Let’s try another one…
• Determine the size of angle A.
135 mm
A
131.5 mm
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Determine an unknown angle
2
• First, label the sides of the triangle...
hypotenuse
135 mm
opposite
A
131.5 mm
adjacent
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Determine an unknown angle
Example 2
• Since you know the lengths of the adjacent
side and the hypotenuse, pick a trig function
that has both of these...
hypotenuse
135 mm
A
131.5 mm
adjacent
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Determine an unknown angle
Example 2
• Which trig function should you pick?
opp
sin A 
hyp
adj
cos A 
hyp
hypotenuse
135 mm
A
131.5 mm
adjacent
You need to pick the
cosine function since it
is the only one that has
both the adjacent side
and hypotenuse in it.
opp
tan A 
adj
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Determine an unknown angle
Example 2
• Now plug-in the numbers you have into the
cosine function...
adj
cos A 
hyp
= 131.5/135 = 0.9740740740…
hypotenuse
135 mm
A = 76.9
A
131.5 mm
adjacent
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End of Presentation
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