Transcript Using Right Triangle Trig

Using Right Triangle
Trigonometry
(trig, for short!)
MathScience Innovation Center
Betsey Davis
Geometry SOL 7
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The student will solve practical
problems using:
Pythagorean Theorem
Properties of Special Triangles
Right Triangle Trigonometry
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
Practical Problem Example 1
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Jenny lives 2 blocks down and 5 blocks
over from Roger.
How far will Jenny need to walk if she
takes the short cut?
R
Pythagorean Theorem
2^2 +5 ^2 = ?
29
So shortcut is
J
29 or about5.4 blocks
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
Practical Problem Example 2
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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
5 3 feet
5 feet
Using Right Triangle Trig
Hypotenuse is 10 feet
She will need 10 feet of
railing
2005 MathScience Innovation Center
B. Davis
Practical Problem Example 3
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Rianna wants to find the angle between
her closet and bed.
We don’t need the
pythagorean theorem
x
It is not a special triangle
100o
We don’t need trig
30o
We just need to know the
3 angles add up to 180
X is 50
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
A
Review
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Find:
Sin A
Cos A
Tan A
13
= 5/13
12
= 12/13
= 5/12
5
S = O/H
C = A/H
Using Right Triangle Trig
T = O/A
2005 MathScience Innovation Center
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If you know the angles,
the calculator gives you sin,
cos, or tan:
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Check MODE to be sure DEGREE is
highlighted (not radian)
Write down
Press SIN 30 ENTER
your 3 answers
Press COS 30 ENTER
Press TAN 30 ENTER
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
What answers did you get?
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Sin 30 = .5
Cos 30 = .866
Tan 30 = .577
These ratios are the
ratios of the legs
and hypotenuse in
the right triangle.
tan
cosSin
30
30=
30
=O/A
A/H
= O/H
== 4/6.93=.577
6.93/8=.866
= 4/8=.5
4 3
30
8
?
or about6.93
60
4?
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
If sin, cos, tan can be found on the
calculator, we can use them to find
missing triangle sides.
50
?
20o
?
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
If sin, cos, tan can be found on the
calculator, we can use them to find
missing triangle sides.
Sin 20 = x /50
50
x
20o
Cos 20 = y/50
Tan 20 = x /y
y
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
Let’s solve for x and y
Sin 20 = x /50
.342 = x/50
17.1 = x
50
x
cos 20 = y/50
.940 = y/50
20o
47 = y
y
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
Do the answers seem reasonable?
No, but the diagram is
not reasonable either.
17.1
50
20o
47
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
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.
? feet
It is not a “special” triangle.
We must use trig !
20o
50 feet
Using Right Triangle Trig
2005 MathScience Innovation Center
B. Davis
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
x feet
So now we know
.364 = x/50
Multiply both sides by 50
20o
50 feet
Using Right Triangle Trig
X = 18.2 feet
2005 MathScience Innovation Center
B. Davis
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?
3 feet
x feet
Using Right Triangle Trig
How long must the
ramp be?
2005 MathScience Innovation Center
B. Davis
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 feet
3 feet
8.33
x feet
Using Right Triangle Trig
o
Y= 3/.145
Y=20.7 feet
2005 MathScience Innovation Center
B. Davis
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
y feet
3 feet
8.33
x feet
Using Right Triangle Trig
o
x= 3/.146
x=20.5 feet
2005 MathScience Innovation Center
B. Davis