Mth 65 – Winter 2015
Section 4.4 through 4.6
4.4 - Introduction to Statistics
Measures of Central Tendency
Mean (page 41)
Median (page 42)
Mode (page 43)
Measures of Dispersion
Range (page 44)
Standard Deviation (page 45)
Rule of Thumb for Standard deviation (page 47)
Direction for one variable statistics entry on pages 45-46. Place the following data sets in
your calculator in lists 1, 2, and 3. Then use STAT CALC to find the one variable
statistics for each data set.
Data Set A: 5, 1, 3, 1, 5
Data Set B: 3, 4, 5, 1, 2
Data Set C: 1, 3, 5, 3, 3
Mean ( x )
Mean ( x )
Mean ( x )
Median
Median
Median
Mode
Mode
Mode
Standard Deviation (σx)
Standard Deviation (σx)
Standard Deviation (σx)
How do the means of set A, set B and set C compare?
What does the standard deviation for each set imply about the points in each set?
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Mth 65 – Winter 2015
Section 4.4 through 4.6
Bob took an age survey in his English class and in his math class. The mean for both
classes was 25.5 years. The standard deviation in his English class was 4.3 years. The
standard deviation in his math class was 7.1 years. Use this information to compare the
ages of the two groups.
Given the two sets of data:
Set A: 25, 30, 35, 50, 60
Set B: 37, 38, 41, 41, 43
Find the mean and the standard deviation for each set.
Set A
x = _____________
Set B
σx = ____________
x = ____________
σx = ____________
How do the means and standard deviations of Set A compare to Set B?
What does the standard deviation for each set imply about the points in the set?
Ms. Roads gave a test last term and the mean was 80%. The standard deviation for the
test was 8. Regina scored 90% on the test. Describe how her score compares to the rest
of the class.
Section 4.5 – Triangles and the Pythagorean Theorem
Types of Angles (page 55)
Acute
Right
Obtuse
Straight
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Mth 65 – Winter 2015
Section 4.4 through 4.6
Types of Triangles: We can classify a triangle by its largest angle. (page 55)
Acute
Right
Obtuse
Pythagorean Theorem (page 57) - Applies only to RIGHT triangles
In the right triangle below angle A and angle B are acute angles. Angle C is the right
angle. The side opposite each angle is named with the same letter written in lower case.
The legs are the two ______________ sides that make the _______________angle. They
are usually called a and b. The hypotenuse is the _____________________ side in the
right triangle and is usually called c. The Pythagorean Theorem says
Use the Pythagorean Theorem, (leg)2 + (leg)2 = (hypotenuse)2 or a2 + b2 = c2, to find
the missing length in each right triangle. Round each answer to 2 decimal places, when
necessary.
6 ft
A
x
4 cm
y
10 ft
6 cm
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Mth 65 – Winter 2015
Section 4.4 through 4.6
The Converse of the Pythagorean Theorem (page 59) gives us a way to tell if a triangle is
a right triangle. It says
Determine whether the following lengths of segment could form a right triangle.
Remember the sum of the squares of the legs must equal the square of the hypotenuse in
a right triangle.
6, 4, 3
9, 15, 12
The Distance formula is based on the Pythagorean Theorem. (page 62)
Find the distance between…
(-1, 4) and (3, 1)
(4, -2) and (-1, 3)
(-5, 7) and (3, 4)
Using Triangles to Solve Problems
The diagonal of a television is 32 inches. If the width of the screen is 25 inches, what is
the height of the screen to the nearest tenth of an inch?
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Mth 65 – Winter 2015
Section 4.4 through 4.6
Triangles are often used in building to add strength. A carpenter framed a wall 12 feet
long and 9 feet high. He needs a diagonal brace to help keep the wall flat before he walks
it into place. How long should the brace be?
Section 4.6 – Sine, Cosine and Tangent Ratios (of the acute angles of a right triangle)
A
c
b
C
B
a
To be able to identify sine, cosine, and tangent ratios in a right triangle, we have to be
able to tell the difference between a leg adjacent to an angle and a leg opposite an
angle. To find a leg adjacent to an angle, the leg must touch the ________________ of
the angle.
Leg adjacent to angle A _____
Leg adjacent to angle B _____
The leg opposite an acute angle is ___________the triangle.
Leg opposite angle A ______
Leg opposite angle B ______
The hypotenuse is still the longest side and is ______________ the right angle. ______
sine of an acute angle of a right triangle =
________________________________________________________
cosine of an acute angle of a right triangle = ______________________________________________________
tangent of an acute angle of a right triangle = _____________________________________________________
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Mth 65 – Winter 2015
Section 4.4 through 4.6
Find the sine, cosine, and tangent ratios for each acute angle in the triangle below.
Use SOH CAH TOA to help you set up each problem.
SOH =
CAH =
TOA =
A
T
25 in
13 cm
5 cm
15 in
20 in
C
A
B
12 cm
F
Sin A =
Sin B =
Sin T =
Sin F =
Cos A =
Cos B =
Cos T =
Cos F =
Tan A =
Tan B =
Tan T =
Tan F =
Finding the Sine, Cosine, and Tangent (ratios) of an (acute) angle on a calculator
First press the Mode key and set your calculator in “degree.” To find the sine of a
angle press sin and the type in the number of degrees the angle measures. The display
will show the sine ratio in decimal form. Use your calculator to evaluate each
trigonometric function. Round your answer to 4 decimal places where appropriate.
Sin 30o =
Cos 45o =
Tan 55o =
Finding a Missing Length in a (Right) Triangle
(when you know the measure of one of the acute angles)
y
10 cm
x
28o
x
35o
y
4.5 cm
x
o
40
y
8.2 cm
cmcm
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Mth 65 – Winter 2015
Section 4.4 through 4.6
Using Trigonometric Ratios to find a Height or a Distance
Draw a picture to help you determine which trig ratio to use.
Bob tethered the kite was flying to the ground on a 150 foot string. If the string makes a
55o angle with the ground, how many feet in the air is the kite?
A ladder leaning against a vertical wall forms a 70o angle with the ground. If the base of
the ladder is 5.1 feet from the wall, to the nearest foot, how long is the ladder?
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