Using Right Triangle Trigonometry (trig, for short!)

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Using Right TriangleTrigonometry(trig, for
short!)

• MathScience Innovation Center
• Betsey Davis

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Geometry SOL 7

• The student will solve practical problems using
• Pythagorean Theorem
• Properties of Special Triangles
• Right Triangle Trigonometry

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Practical Problem Example 1

• Jenny lives 2 blocks down and 5 blocks over from
  Roger.
• How far will Jenny need to walk if she takes the
  short cut?

Pythagorean Theorem22 5 2 ? 29 So shortcut
is
R
J
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Practical Problem Example 2

• Shawna wants to build a triangular deck to fit in
  the back corner of her house.
• How many feet of railing will she need across the
  opening?

Special 30-60-90 triangle Hypotenuse is 10
feet She will need 10 feet of railing
5 feet
Railing across here
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Practical Problem Example 3

• Rianna wants to find the angle between her closet
  and bed.

We dont need the pythagorean theorem It is not a
special triangle We dont need trig We just need
to know the 3 angles add up to 180 X is 50
x
100o
30o
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Review
A
13

• Find
• Sin A
• Cos A
• Tan A

12
5/13
12/13
5/12
5
S O/H C A/H T O/A
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If you know the angles,the calculator gives you
sin, cos, or tan

• Check MODE to be sure DEGREE is highlighted (not
  radian)
• Press SIN 30 ENTER
• Press COS 30 ENTER
• Press TAN 30 ENTER

Write down your 3 answers
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What answers did you get?
These ratios are the ratios of the legs and
hypotenuse in the right triangle.

• Sin 30 .5
• Cos 30 .866
• Tan 30 .577

Sin 30 O/H 4/8.5
cos 30 A/H 6.93/8.866
tan 30 O/A 4/6.93.577
30
8
?
60
?
4
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If sin, cos, tan can be found on the calculator,
we can use them to find missing triangle sides.
50
?
20o
?
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If sin, cos, tan can be found on the calculator,
we can use them to find missing triangle sides.
Sin 20 x /50 Cos 20 y/50 Tan 20 x /y
50
x
20o
y
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Lets solve for x and y
Sin 20 x /50 cos 20 y/50
.342 x/50 17.1 x
50
x
.940 y/50 47 y
20o
y
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Do the answers seem reasonable?
No, but the diagram is not reasonable either.
50
17.1
20o
47
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Practical Problem Example 4
Jared wants to know the height of the flagpole.
He measures 50 feet away from the base of the
pole and can see the top at a 20 degree angle.
How tall is the pole?
Pythagorean Theorem does not work without more
sides. It is not a special triangle. We must
use trig !
20o
50 feet
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Practical Problem Example 4
Which of the 3 choices sin, cos, tan uses the
50 and the x????
Tan 20 x/50 Press tan 20 enter So now we
know .364 x/50 Multiply both sides by 50 X
18.2 feet
20o
50 feet
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Practical Problem Example 5
Federal Laws specify that the ramp angle used for
a wheelchair ramp must be less than or equal to
8.33 degrees.
You want to build a ramp to go up 3 feet into a
house. What horizontal space will you need? How
long must the ramp be?
3 feet
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Practical Problem Example 5
You want to build a ramp to go up 3 feet into a
house. What horizontal space will you need? How
long must the ramp be?
Sin 8.33 3/y .145 3/y .145y 3 Y
3/.145 Y20.7 feet
3 feet
8.33 o
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Practical Problem Example 5
You want to build a ramp to go up 3 feet into a
house. What horizontal space will you need? How
long must the ramp be?
tan 8.33 3/x .146 3/x .146x 3 x
3/.146 x20.5 feet
3 feet
8.33 o