Transcript GridIron Girls

Presented by
Dr. Del Ferster
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We’ll spend some time on an “INTRO” to
trig.
I have a video to show you, in case you are
inclined to teach trig to your students.
We’ll work on the TRIG RIVER ACTIVITY
We’ll work on some “test-like” questions
◦ I know that we usually do these first, but I
believe that we’ll benefit more by
spending some time looking at the basics
of trigonometry together. 
3 Basic Trigonometric Functions
SINE
COSINE
TANGENT
Greek Letter q
Prounounced
“theta”
Represents an unknown angle
The most important skill you need
right now is the ability to correctly
label the sides of a right triangle.
 The names of the sides are:
◦ the hypotenuse
◦ the opposite side
◦ the adjacent side
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The hypotenuse is easy to locate because it is
always found across from the right angle.
Since this side is
across from the right
angle, this must be
the hypotenuse.
Here is the
right angle...
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Before you label the other two sides you must
have a reference angle selected.
Lots of books label this as q
It can be either of the two acute angles.
In the triangle below, let’s pick angle B as the
reference angle.
B
A
This will be our
reference angle...
C
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Remember, angle B is our reference angle.
The hypotenuse is side BC because it is
across from the right angle.
B (ref. angle)
hypotenuse
A
C
Labeling Right Triangles

Side AC is across from our reference
angle B. So it is labeled: opposite.
B (ref. angle)
hypotenuse
A
C
opposite
Labeling Right Triangles
Adjacent means beside or next to
 The only side unnamed is side AB. This
must be the adjacent side.
B (ref. angle)
adjacent
hypotenuse
C
A
opposite
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Let’s put it all together.
Given that angle B is the reference angle, here
is how you must label the triangle:
B (ref. angle)
hypotenuse
adjacent
C
A
opposite
 Given
the same triangle, how
would the sides be labeled if
angle C were the reference
angle?
 Will there be any difference?
Labeling Right Triangles
Let’s put it all together.
 Given that angle C is the reference
angle, here is how you must label the
triangle:

B
hypotenuse
opposite
C (ref. angle)
A
adjacent
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Given that angle X is the reference angle,
label all three sides of triangle WXY.
Do this on your own. Click to see the
answers when you are ready.
W
Y
X
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How did you do?
W
adjacent
opposite
hypotenuse
Y
X
Using trig functions to
find the length of a
missing side.
A surveyor is standing 50 feet from the base of a large
tree. The surveyor measures the angle of elevation
to the top of the tree as 71.5°. How tall is the tree?
Opp
tan 71.5° 
Hyp
y
71.5°
50
y
tan 71.5° 
50
y = 50 (tan 71.5°)
y = 50 (2.98868)
y  149.4 ft
A person is 200 yards from a river. Rather than walk
directly to the river, the person walks along a straight path
to the river’s edge at a 60° angle. How far must the
person walk to reach the river’s edge?
cos 60°
x (cos 60°) = 200
200
60°
x
x
X = 400 yards
Using trig functions to
find the measure of one
of the acute angles.
1.
Redraw the figure and mark on it HYP, OPP,
ADJ relative to the unknown angle
OPP
HYP
2.67
km
q
ADJ
2.
3.
For the unknown angle choose the correct trig ratio which can be
used to set up an equation
Set up the equation
OPP
q
2.67
km
HYP
ADJ
4.
Solve the equation to find the unknown
using the inverse of trigonometric ratio.
OPP
q
2.67
km
HYP
ADJ
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Find, to one decimal place, the unknown angle in the
triangle.
q
3.1 km
2.1
km
q  34.1
o
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Find, to 1 decimal place, the unknown angle in the
given triangle.
4m
q
7m
q  29.7
o