right s and trigonometry 7 pythagorean theorem the determine right triangles 6 pythagorean theorem,...
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Right s and trigonometry7 Pythagorean Theorem the determine right triangles6 Pythagorean Theorem, solve sides 5 WP: Pythagorean Theorem4 Special Right Triangles3 Sine, Cosine and Tangent ratios2 Trig to solve sides in a 1 WP: TrigonometryUnit Review
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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
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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
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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)
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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
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6 Pythagorean theorem
A Whip!
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6a Pythagorean theoremRemember 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 __________
Hypotenusec
hypotenuse
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6b Pythagorean theorem
10
8
Ex1. Find the missing side of the triangle
82+102=h2 From Pyth theorem
64+100= h2 Solve
164= h2
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
8
a
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5 WP: Pythagorean theoremImagine a bridge that spans a canyon of two miles. (5280 feet = 1 mile)
2 mile bridge
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
What is the height?(Approx)
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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.
(New
Stre
et)
Main St.
N. B
lvd
3 mi.
8 mi.
82+32=c2
64+9=c2
73=c2
73=c
The new road is 73 mi.
(73)(5280) (x) by feet/mi.
(45112.339)($100)
$4,511,233.90 Approx
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5b WP: Pythagorean theoremEx2. 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?
20 mi
21 mi
Ferris
Dunlap Butte
?
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4 Special Right Triangles
Do you have a calculator with Sin, Cos
& Tan buttons?
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4a 45-45-90 Triangles
||
=
What are the degree measures of this ?
45°
45°
If we had a leg length of 1, what is the hypotenuse?(Use Pythagorean theorem) _______
1
12
If we had a leg length of 10, what is the hypotenuse? ______
0
102
Using the Pythagorean theorem we can conclude:
P
P||
= P2For all 45-45-90 s
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4b 30-60-90 Triangles
60°
30°
5
10w
Using the Pythagorean theorem, find “w”! NOW!!!
52+w2=102
25+w2=100
w2=75w=75
75/ \
25 3
53
53
60°
Using the Pythagorean theorem, we can conclude:
P
2PP3For all 30-60-90 triangles
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4c 45-45-90 Triangles
Ex1. In ABC, A is a right angle and mB=45°. If AB=36 feet, find BC.
A B
C
45°36 ft
BC=362
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4d 30-60-90 Triangles
30°
60°
P
2PP3
Ex2. In a 30-60-90 triangle, the hypotenuse is 28 feet,
What is the shorter leg? ___________14 feet
What is the longer leg? ___________143
28
14
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3 Sine, Cosine & Tangent ratios
Bible trivia time…….How many years did Moses wonder the desert before he entered the promised land?
Moses reached the promised land, however, God forbade him entrance.
How many wise men went to see Jesus?
We don’t know, we only know of the mention of three gifts.
25 point reward for turning in calculators that are
missing from my class…!
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3a Sine, Cosine & Tangent ratios
Some Old Hippie, Came A Hopping, Through Our Alley
S C Tine os an= = =OppositeHypotenuse
AdjacentHypotenuse
OppositeAdjacent
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
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3b Sine, Cosine & Tangent ratios
A
BC9
12 15
Is this a right ? _________yes
Why? _______________Since a2+b2 = c2
What is the Sine of A? ___________9/15 = 3/5
What is the Cos of A? ___________12/15 = 4/5
What is the Tan of A? ___________9/12 = 3/4
S C TO A OH H A
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3c Sine, Cosine & Tangent ratios
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3d Sine, Cosine & Tangent ratios
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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….!
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2a Trig to solve sides in a
Remember
27° 7
x
Solve for x.
Which side are we looking for? a o h
Which side do we have? a o h
Since Cos uses “a” and “h”, we are going to use the Cos function
Cos27= 7x
(cos27) (x)= 7 Cross Mulitply x7.86
PS. means approx equal
S C TO A OH H A
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2b Trig to solve sides in a
25°7
x
Solve for x
What sides are we working with in reference to the angle? O & A
Tan25= X7
(Tan 25) (7) = x
3.26 x
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2c Trig to solve sides in a Ex3. Given A = 47 and c = 12, find a, to the nearest tenth.
A
BC a
b c47°
12
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1 WP: Trigonometry
What do veterinarians usually call little cats with white, black, red and cream colored coats?
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1a WP: Trigonometry
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1b WP: TrigonometryEx1. 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°
?
3.4m
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1c WP: TrigonometryEx2. 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.
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1d WP: TrigonometryEx3. 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?
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Unit 8 Review
If a2+b2=c2 is true, then it is a right triangle.
Pythagorean Theorem – Given length of two sides. c
P
P||
= P2
For all 45-45-90 s
60°
P
2PP3
For all 30-60-90 triangles
When give a Degree and the length of a side.
S C TO A OH H A