Transcript 91 Pythagorean theorem

Right s and trigonometry
7 Pythagorean Theorem the determine right triangles
6 Pythagorean Theorem, solve sides
5 WP: Pythagorean Theorem
4 Special Right Triangles
3 Sine, Cosine and Tangent ratios
2 Trig to solve sides in a 
1 WP: Trigonometry
Unit Review
7 Pythagorean Theorem to
determine right triangle
What is the proper
pronunciation for the second
day of the week?
a) TEE-USE-DAY
b) CHOOSE-DAY
c) TWOS-DAY
d) None of the above
7a Pythagorean Theorem to
determine right triangle
If the Pythagorean theorem works for 3 numbers (“c” will
always be the largest), then these values form a right triangle.
If a2+b2=c2 is true, then it is a right triangle
Keep in mind that C will ALWAYS be the longest side
7b Pythagorean Theorem to
determine right triangle
Ex1. How many of the triples below could be sides of a right triangle?
(14, 48, 49)
(33, 56, 65)
(9, 41, 40)
(45, 36, 27)
7c Pythagorean Theorem to
determine right triangle
Ex2. Which of the triangles described in the table is a right triangle?
Side 1 Side 2 Side 3
Triangle Q
10
8
6
Triangle R
11
8
19
Triangle S
10
8
164
Triangle T
110
11
10
6 Pythagorean theorem
A Whip!
6a Pythagorean theorem
Remember this…..
a2+b2=c2
What does the letter “c” represent? __________
Hypotenuse
What does “a” and “b” represent? _______________
The legs of the 
This only applies to right triangles!
The side opposite the right angle is the __________
hypotenuse
6b Pythagorean theorem
Ex1. Find the missing side of the triangle
82+102=h2
From Pyth theorem
64+100= h2 Solve
8
164= h2
10
Ex2.  ABC is a right triangle with hypotenuse c and legs of
length a and b. If b = 8 and c =10, then a = _____.
10
a
8
5 WP: Pythagorean theorem
Imagine a bridge that spans a canyon of two
miles. (5280 feet = 1 mile)
Unfortunately they forgot to place expansion
joints into the bridge and when it gets hot, the
bridge expands exactly one foot.
How high does the bridge bow upward with this expansion?
2 mi + 1 foot bridge
2 mile bridge
What is the height?
(Approx)
5a WP: Pythagorean theorem
Draw a picture and label it!!!!
The city commission wants to construct a new street that
connects Main Street and North Boulevard as shown in the
diagram below. The construction cost has been estimated
at $100 per linear foot. Find the estimated cost for
constructing the street.
82+32=c2
N. Blvd
8 mi.
3 mi.
64+9=c2
73=c2
73=c
Main St.
The new road is 73 mi.
(73)(5280) (x) by feet/mi.
(45112.339)($100)
$4,511,233.90 Approx
5b WP: Pythagorean theorem
Ex2. Janina used the diagram to compute the distance from Ferris to
Dunlap to Butte.
How much shorter is the distance directly from Ferris to Butte than
the distance Janina found?
Ferris
?
20 mi
Dunlap
21 mi
Butte
4 Special Right Triangles
Do you have a
calculator with Sin, Cos
& Tan buttons?
4a 45-45-90 Triangles
What are the degree measures of this ?
45°
If we had a leg length of 1, what is the hypotenuse?
(Use Pythagorean theorem) _______
12
=
||
10
45°
If we had a leg length of 10, what is the hypotenuse? ______
102
Using the Pythagorean theorem we can conclude:
P2
=
P
||
P
For all 45-45-90 s
4b 30-60-90 Triangles
30°
w
53
Using the Pythagorean theorem, find “w”! NOW!!!
10
60°
5
52+w2=102
25+w2=100
w2=75
w=75
75
/ \
25 3
53
Using the Pythagorean theorem, we can conclude:
P3
2P
60°
P
For all 30-60-90 triangles
4c 45-45-90 Triangles
Ex1. In ABC, A is a right angle and mB=45°.
If AB=36 feet, find BC.
A
36 ft
B
45°
BC=362
C
4d 30-60-90 Triangles
Ex2. In a 30-60-90 triangle, the hypotenuse is 28 feet,
30°
P3
2P
28
What is the shorter leg? ___________
14 feet
14 60°
P
What is the longer leg? ___________
143
3 Sine, Cosine & Tangent
ratios
Bible trivia time…….
25 years
point
reward
for
How many
did Moses
wonder
the turning in
desert before he entered the promised land?
calculators that are
Moses missing
reached the promised
land,
however,
God
from
my
class…!
forbade him entrance.
How many wise men went to see Jesus?
We don’t know, we only know of the mention of
three gifts.
3a Sine, Cosine & Tangent
ratios
Remember this and you will have it easy…!
Adjacent - The leg touching the angle
Opposite - Leg opposite the angle
Hypotenuse - Side opposite the right angle
Some Old Hippie, Came A Hopping, Through Our Alley
Opposite
ine= Hypotenuse
S
C
Adjacent
os = Hypotenuse
Opposite
an = Adjacent
T
3b Sine, Cosine & Tangent
ratios
yes
Is this a right ? _________
A
Why? _______________
Since a2+b2 = c2
O
SH
12
A
CH
O
TA
15
9/15 = 3/5
What is the Sine of A? ___________
12/15 = 4/5
What is the Cos of  A? ___________
C
B
9
9/12 = 3/4
What is the Tan of  A? ___________
3c Sine, Cosine & Tangent
ratios
3d Sine, Cosine & Tangent
ratios
2 Trig to solve sides in a 
I am thinking of two common objects,
they both carry out the same function,
but one has thousands of moving parts
and the other has no moving parts.
What are these items?
Hurry, times a wasting….!
2a Trig to solve sides in a 
O
Remember S H
27° 7
A
CH
O
TA
Solve for x.
Which side are we looking for? a o h
x
Which side do we have? a o h
Since Cos uses “a” and “h”, we are going to use the Cos function
Cos27= 7
x
(cos27) (x)= 7
 x7.86
Cross Mulitply
PS.  means approx equal
2b Trig to solve sides in a 
7
Solve for x
25°
x
What sides are we working with in reference to the angle? O & A
Tan25= X
7
(Tan 25) (7) = x
3.26  x
2c Trig to solve sides in a 
Ex3. Given A = 47  and c = 12, find a, to the nearest tenth.
A
47°
b
12
C
a
c
B
1 WP: Trigonometry
What do veterinarians
usually call little cats
with white, black, red
and cream colored
coats?
1a WP: Trigonometry
1b WP: Trigonometry
Ex1. A slide 3.4 m long makes an angle of 35 with the ground.
How high is the top of the slide above the ground?
?
35°
1c WP: Trigonometry
Ex2. A ladder leans against a building forming an angle of 60
with the ground. The base of the ladder is 4 feet from the
building. Find the length of the ladder.
1d WP: Trigonometry
Ex3. A ladder 14 feet long makes an angle of 53 with the
ground as it leans against a barn. How far up the barn does the
ladder reach?
Unit 8 Review
Pythagorean Theorem – Given length of two sides.
If a2+b2=c2 is true, then it is a right triangle.
For all 45-45-90 s
P3
P2
=
For all 30-60-90 triangles
2P
P
60°
||
P
P
When give a Degree and the length of a side.
O
SH
A
CH
O
TA
c