Math Pages 125-127

Percent:

-Means out of 100
-Another name for hundredths
-65% means 65 out of 100 or 65/100 or 0.65


Fractional Percent:

-A percent that includes a portion of a percent such as 7 3/8% or 4.5%

Page 125 Show you Know

A) 248%=
B) o.4%=
C) 74.8%=


Page 127 Show you Know

A)




B)


C)

Duyen's Math Scribe Post: Pages 110 & 111 Questions 3, 9, 13

Sorry for the bad quality because when I converted the PowerPoint to AuthorStream then to Youtube, it just killed the original quality. Also if you notice the words might seem squished or cut well it's not. It's just that when AuthorStream converted the file it converted it to make it fit to a smaller screen. By the way it's suppose to have music, but it didn't work on Authorstream.

Watch
http://www.youtube.com/watch?v=iFPsqk8MYj0

http://www.youtube.com/watch?v=FUhpIS8YTfc

http://www.youtube.com/watch?v=ku4rEwRxZOc

http://www.youtube.com/watch?v=kBw_i6tlQfU


Play
http://www.quia.com/jg/65631.html

http://resources.oswego.org/games/



Search
http://www.mathsisfun.com/square-root.html

http://staff.argyll.epsb.ca/jreed/math8/strand1/1105.htm

Paulo's Textbook Post page 110-111 numbers 3 7 11

a) Maria walked 420m

b) Walter walked 323m

c) Maria walked 97m further.

c² - b² = a²

80² -79² = a²

6400 - 6241 = a²

159 = a²

√159 = √a²

12.6 = a

The minimum distance is 279.1cm and the maximum distance is 291.7cm

Pythagoras Theorem

Raelynn's Homework Book Post: pg. 33 Numbers 4,6,7

Pythagorean Relationship.
Homework Book pg. 33
Numbers 4, 6, 7.


4.) The foot of a ladder is 1m from a wall. If the ladder is 6cm long, how far up the wall does the ladder reach? Give the answer to the nearest tenth of a metre. Show your work.


a² - b² = c²
6² - 1² = c²
(6x6) - (1x1) = c²
36cm² - 1cm² = 35 cm²
35cm² = c²
√35cm² = √c²
5.9cm² = c² (round up will be 6)

It will be 5.9/6 far up the wall.




6.) The width of a rectangle is 8cm, and its diagonal is 17cm.










a) Calculate the length of the rectangle. Show your work.
c² - b² = a²
17² - 8² = a²
(17x17) - (8x8) = a²
289cm² - 64cm² = 225cm²
225cm² = c²
√225cm² = √c²
15cm² = c²

b) Calculate the area of the rectangle.
120cm²


7.) A quadrilateral has a width of 17cm and a length of 26cm. A diagonal is 31cm. Is the quadrilateral a rectangle? Justify your answer.



a² + b² = c²
26² + 17² = c²
(26x26) + (17x17) = c²
676cm² + 289cm² = 965cm²
965cm² = c²
√965cm² = √c²
31.06cm²

Answer: No, the corners do not meet at right angles because 17² + 26² ≠ 31²



Enjoy this video. Hope it helps.

Shane's Textbook Post Pages 103-105. Numbers 7,10,13,15

a.)

h² + g² = r²
h² + 5² = 9²
h² = 9² - 5²
h² = (9x9) - (5x5)
= 81-25 = 56
= √h² = √56 mm²
= h = 7.48 mm

b.)

p² + q² = r²
p² + 11² = 15²
p² = 15² - 11²p
p² = (15x15) - (11x11)
= 225 - 121 = 104
= √p² = √104 mm²
= 10.20

 a² + b² = c²
27 m² + 27 m² = c²
(27x27) + (27x27)
729 + 729 = c²
1458 m²
√1458 m² = √c²
38.18 m²
 

a² + b² = c²
8² + b² = 10 mm
b² = 10² - 8²
b² = (10x10) - (8x8)
= 100 - 64 = 36
= √b² = √36 mm²
= b = 6 mm

a² + b² = c²
=22 + 42 = c²
=4 + 16 = c²
=20 = c²
The square root of 20 = c²
c² = 4.47

Homework Book : Even Questions

a) a² = c² - b²
a² = 26² - 24²
a² = 676 - 576
a² = 100m²
√100m² = √a²
10m = a



b) b² = c² - a²
b² = 39² - 15²
b² = 1521 - 225
b² = 1296cm²
√1296cm² = √b²
36cm = b





a) a² + b² = c²
8² + 9² = c²
64 + 81 = c²
145cm² = c²
√145cm² = √c²
12cm = c


b) a² + b² = c²
6² + 10² = c²
36 + 100 = c²
136cm² = c²
√136cm² = √c²
12cm = c


I thought of the height as the line going upwards↑, the base as the bottom_, and the hypotenuse is the longest leg. I used B as the unknown height.
b² = c² - a²
b² = 11² - 4²
b² = 121 - 16
b² = 105cm²
√b² = √105cm²
b = 10.2m



No the ramp is not a right triangle because the areas of the legs added up to 13m². The area of the hypotenuse on the other hand was 25m². For the shape to be a right triangle the two values would have to be equal.





Here is a video and a link to a fun-filled Pythagoras game. ←Click that for the game ☺



P.S if you see a √ its a square root symbol.

Trisha's Textbook pages (:

Pg. 103 - 105
# 6, 9, 12 and 15

6. Determine the length of the leg for each right triangle.


a)
a2 + b2 = c2
72 + 252 = c2
49 + 625 = c2
674 =c2
The square root of 674cm = c2
25.96 cm = c

b)

T2 - S2 = R2

262 - 242 = R2

676 - 576 =R2
100 = R2

The square root of 100 cm = c2
10cm = R2







9. Tina wants to construct a path along the diagonal of her yard. What length will the path be? Express your answer to the nearest tenth of a meter.


a2 + b2 = c2
62 + 122 = c2
36 + 144 = c2
180 = c2
The square root of 180 = c2
13.41 = c






12. The hypotenuse of the triangle cuts the circle in half. What is the diameter of the circle?

a2 + b2 = c2
72 + 52 = c2
49 + 25 = c2
74 = c2
The square root of 74 = c2
8. 60




15. The coordinate grid shown was drawn centimeter grid paper. What is the length of lime segment AB?



A and B segment looks like a right triangle.

a2 + b2 = c2
22 + 42 = c2
4 + 16 = c2
20 = c2
The square root of 20 = c2
4.47 = c




Special thanks to Anabelle for helping me out (:
Thanks.

Patrick's Textbook Post Pages 103-105. Numbers 5,8,11,14

area of square = a²
area of square = 6x6
area of square = 36cm²

area of square = b²
area of square = 8x8
area of square = 64cm²

a² + b² = c²
6² + 8² = c²

36 + 64 = c²
100cm² = c²



√100cm² = √c²
10cm = c

a² + b² = c²

50² + 200² = c²
2500 + 40 000 = c²
42500 cm² = c²
√42500 cm² = √c²

206 cm = c

√914 = √c²
30.2 cm = c

c² - a² = b²
30.2² - 17² = b²
912 - 289 = b²
623 cm² = b²
√623 cm² = √b²

25 cm = b

perimeter = a + b + c
perimeter = 17 + 25 + 30.2
perimeter = 72.2

b²=c²-a²
b²=5²-3²
b²=25-9
b²=16m²
√b²=√16m²
b=4m

c²=a²+b²
c²=6²+4²
c²=36+16
c²=52m²
√c²=√52m²
c=7.2m
The length of c is 7.2m.

Homework Book: Odd Questions

1) The _______ relationship can be used to determine the _______ of the _________
of a right triangle when the lengths of the two_______ are known.

pythagorean, lengths, hypotenuse, legs

3)Determine the length of each hypotenuse.show your work.
A)












a²+b²=c²
9cm²+40cm²=c²
9x9+40x40=c²
81cm²+1600cm²=c²
1681cm²=c²
√1681cm²=√c²
41cm=c












B)












a²+b²=c²
12m²+35m²=c²
12x12+35x35=c²
144m²+1225m=c²
1369m²=c²
√1369m²=√c²
37m=c











5)Calculate the missing side length for each right triangle, to the nearest tenth of a centimetre. Show your work.
A)











c²-a²=b²
6cm²-5cm²=b²
6x6+5x5=b²
36cm²+25cm²=b²
11cm²=b²
√11cm²=√b²
3.3cm=b











B)











c²-b²=a²
12cm²-7cm²=a²
12x12+7x7=a²
144cm²+49cm²=a²
95cm²=a²
√95cm²=√a²
9.7cm=a












7)A triangle is made up of two smaller congruent right triangles.












A)Find the length of the hypotenuse for the right triangles, to the nearest tenth of a metre. Show your work.
a/2=a²
8/2=4

a²+b²=c²
4²+2²=c²
4x4+2x2=c²
16m²+4m²=c²
20m²=c²
√20m²=√c²
4.5m=c

B)Calculate the perimeter of the large triangle, to the nearest tenth of a metre. Show your work.
a+b=perimeter
8+4.5=17 m

Here is a link about Pythagorean Relationship.

Here is a video using math link textbook about pythagorean relationship.

Finding Side Lengths

A baseball diamond is a square. How could you determine the distance
from second base to home plate? How many different strategies can
you develop?Determine the length of leg s of the
right triangle

a2+ b2= c2

(27x27) + (27x27) = c2

729m(squared) + 729m(squared)

c21458= c2

1158cm(squared

c238.18m= c

• The Pythagorean relationship can be used to determine the length of the hypotenuse of a right triangle when the lengths of the two legs are known.

a2+b2=c2

3cm+4cm=c2

3x3=9

4x4=16

9+16=25cm

25 square root=5

c=5

• The Pythagorean relationship can be used to determine the leg length of a right triangle when the lengths of the hypotenuse and the other leg are known.

p2 + q2 = r2
p2 + 122 = 152
p2 + 144 = 225
p2 + 144 - 144 = 225 - 144
p2 = 81
p = √
___
81
p = 9

1. Jack must determine the missing side length of a triangle. He decides to draw it and then measure it, as shown. Do you agree with the method that Jack is using? Explain

I do not agree because, one it would take to long, two when I drew a triangle on grid paper it was very hard to measure the hypotenuse, also its just a lot quicker to use Pythagorean relationships.

2.Kira calculated the missing side length of the right triangle.

y2 = 52+132

y2 = 25
169y2 = 194y2

≈ 13.9

The length of side y is approximately 13.9 cm. Is Kira correct? If she is correct, explain how you know. If she is incorrect,explain the correct method.

Kira is correct because 5x5=25 and 13x13=16

169+25=194

194 square root= 13.9

3. Determine the length of each hypotenuse.

a)

a2+b2=c2

a=12cm 12cm+16cm=c2

b=16cm 12x12=144cm

20cm 16x16=256

144+256=400

400 squared=20

b)

c2-a2=b2

a=16m 30m-16m-c2

b=25.3m 30x30=900

c=30m 16x16=256

900-256=644

644 square root=25.3

4. What is the length of each hypotenuse?
Give your answer to the nearest tenth of
a centimetre.

a)

a=6cm a2+b2=c2

b=7cm 6cm+7cm=c2

c=9.2cm 6x6=36

7x7=49

36+49=85
85 square rooted=9.2

b)

c2-b2=a2

a=7.5cm 11cm-8cm=a2

b=8cm 11x11=121

c=11cm 8x8=64

121-64=57

57 square rooted=7.5