Transcript AMSTI - handsonmath8

Problem of the Day
• In what ways is the
Pythagorean Theorem
useful. Give two
examples from real life.
4.1 Stopping Sneaky
Stephanie
Baseball History
• Although most people consider
baseball an American invention, a
similar game, called rounders, was
played in England as early as the
1600s. Like baseball, rounders
involved hitting a ball and running
around bases. However, in rounders,
the fielders actually threw the ball at
the base runners. If a ball hit a
runner while he was off base, the
runner was out.
Baseball History
• Alexander Cartwright is considered the father of
organized baseball. He started the
Knickerbockers Base Ball Club of New York in
1845 and wrote an official set of rules.
According to Cartwright’s rules, a batter was out
if a fielder caught the ball either on the fly or on
the first bounce. Today, balls caught on the first
bounce are not outs. Cartwright’s rules also
stated that the first team to have a total of 21
runs at the end of an inning was the winner.
Today, the team with the highest score after nine
innings wins the game.
Scenario
• Kathy is the catcher for the AMSTI Ants baseball
team. Stephanie, from the ACOS Astros, is on
first base. Stephanie is known for stealing
bases, so Kathy is keeping a sharp eye on her.
• The pitcher throws a fastball, and the batter
swings and misses. Kathy catches the pitch.
Out of the corner of her eye, she sees Stephanie
take off for second base.
• How far must Kathy throw the baseball to get
Stephanie out at second base?
Take Me Out to the Ball Game
• Does anyone know the distance between
bases on a standard baseball field?
90 ft
90 ft
90 ft
90 ft
How far do you think a catcher would need to
throw the ball to get a runner out at second base?
Problem 4.1
90 ft
127 ft
90 ft
The shortstop on a baseball team stands halfway between
second and third base. How far is the shortstop from home?
Problem 4.1
Follow-up
45 ft
101 ft
90 ft
ACE Problems pg 46-49 #’s1, 3, 5, 6
• 1a. a2 + b2 = c2
5002 + 6002 = c2
250000 + 360000 = 610000
√610000 = 781 m
• 1b. 1100 – 781 = 319 m
• 3. a2 + b2 = c2
152 + b2 = 252
225 + b2 = 625
-225
-225
b2 = 400
√400 = 22 ft
ACE Problems 1, 3, 5, 6
• 5. a2 + b2 = c2
32 + 42 = c2
9 + 12 = c2
25 = c2
√25 = 5 cm (bottom diagonal)
52 + 122 = c2
25 + 144 = c2
169 = c2
√169 = 13 cm
ACE Problems 1, 3, 5, 6
• 6. a2 + b2 = c2
62 + 72 = c2
36 + 49 = c2
85 = c2
√85 = Bottom Diagonal
√(85)2 + √(111)2 = c2
85 + 111 = c2
196 = c2
√196 = 14
Journal Writing
• Explain to a 7th grader using words and
pictures how far it is for a catcher to throw
out a runner at 2nd base.
4.2 Analyzing Triangles
• An equilateral (“EQUAL” lateral) triangle has all
same
three sides the _________
length.
• The angles in an equilateral triangle have the
same
_________
measure.
• What is true about the sum of the angles of ANY
triangle. They add up to __________.
180˚
• What is the measure of each angle in ANY
60˚
equilateral triangle ______________?
Equilateral Triangle
A
Problem 4.2
A. Since all sides and angles are
equal in an equilateral triangle, ABP
and ACP are congruent.
B. APB=90˚,
ABP=60˚,
PAB=30˚
D. BC & AP are perpendicular
E. Length of side opposite a
30˚ angle in a right triangle
is half the length of the
hypotenuse, and longer
leg is √3 times the shorter
leg
2
2
C. AB=2, BP=1,
AP=√3 (22+1 2=3)
C
B
2
Problem 4.2
Follow-up
1.
1.
Length of side opposite 30˚ is
half the hypotenuse=3; Since
a2+32=62 a2=27 a=√27
2.
2.
a. They are congruent.
A
B
b. 45, 45, 90 because the
diagonal divides the 90 into 2
angles of 45 each.
c. Since each side is 1,
12+12=2 hypotenuse = √2
d. Angles still 45, 45, 90;
however, 52+52=50
hypotenuse = √50.
D
C
ACE Problems Pg 47-49 #’s 2 & 4
• 2. a2 + b2 = c2
152 + 152 = c2
225+225= c2
√450 = 21.2 m
21.2+(1000-30)+21.2 = 1012.4m
• 4. Since the length of the side opposite the 30˚ angle is ½
the hypotenuse, the hypotenuse is 58*2=116ft.
a2 + 582 = 1162
a2 = 10092
√10092 = 100.5 ft
100.5 + 5 = 105.5 ft
Alabama Course of Study
• Which course of study
objectives did we cover
in today’s lesson?
Summary
• We showed how the Pythagorean
Theorem can be used in real life. Can you
think of other examples where it might be
used?
• We investigated properties of some
special right triangles, including a 30-6090 triangle and an isosceles right triangle,
by applying the Pythagorean Theorem.
Websites
• www.wikimedia.org
• www.baseballalmanac.com/poetry/po_case.shmtl
• www.archive.org/details/shortpoetry_021_l
ibrivox
• Smartboard Notebook Tools (for shapes)