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Trigonometry
Basic Calculations of Angles and
Sides of Right Triangles
1
Use trigonometry to determine the size
of an angle.
2
Determine an unknown angle
Example 1
• To start, we will determine the size of an
unknown angle when two sides of the right
triangle are known.
5.5”
A
12”
3
Determine an unknown angle
Example 1
• Let the unknown angle A be the reference
angle.
5.5”
A
12”
4
Determine an unknown angle
Example 1
• Now label the sides of the right triangle...
opposite
5.5”
hypotenuse
A
adjacent 12”
5
Determine an unknown angle
Example 1
• Note that we only know the lengths of the
opposite and adjacent sides.
opposite
5.5”
hypotenuse
A
adjacent 12”
6
Determine an unknown angle
Example 1
• So we need to pick a trig function that has
the opposite and adjacent sides in it...
opposite
5.5”
A
adjacent 12”
7
Determine an unknown angle
Example 1
• Which trig function should you pick?
opp
sin A 
hyp
opposite
adj
cos A 
hyp
5.5”
A
12”
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.
8
Determine an unknown angle
Example 1
• Now plug-in the numbers you have into the
tangent function...
opp
tan A 
adj
5 .5
tan A  0.458333...
tan A 
12
tan 1 (tan A)  tan 1 (0.458333...)
opposite
5.5”
A = 24.6°
A
adjacent 12”
Now use your
calculator to
solve. Type-in
.458333, press the
2nd function key,
then press the tan
key
9
Determine an unknown angle
Example 1
• How could you determine the size of the
remaining angle?
…this one must be 65.4° degrees.
(Since 180° - 90° - 24.6° = 65.4°)
65.4°
5.5”
..and this one
was computed
to be 24.6°…
This angle is
90°…
24.6°
12”
10
Determine an unknown angle
Example 2
• Let’s try another one…
• Determine the size of angle A.
35 mm
A
31.5 mm
11
Determine an unknown angle
Example 2
• To determine the other angle:
• 180° - 90° - 25.8° = 64.2°
35 mm
64.2°
25.8°
31.5 mm
17
Determine an unknown angle
Example 3
• Let’s try one more.
• Determine the size of angle A.
125 mm
132 mm
A
18
Determine an unknown angle
Example 3
• The angle is computed to be 18.7°.
125 mm
18.7°
132 mm
71.3°
24
Homework
pg. 485 #3
pg. 486 #7, 10,12,14,19,20
32