Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples...
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Transcript of Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples...
![Page 1: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/1.jpg)
JOURNAL 7 & 8Maria Elisa Vanegas 9-5
![Page 2: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/2.jpg)
RATIOA ratio is a comparison of 2 things it could be 2 values.
Examples1. A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3
2. A(-1,3) B(1,4) rise 3-4 -1 1 run = -1-1 = -2 = 2
3. A(-2,-2) B(2,2) rise -2-2 -4 1 run = -2-2 = -4 =
PROPORTIONA proportion is simply a equation that tells us that 2 ratios are equal to each other. You solve proportions by cross multiplying the given fractions and then simplifying. You can check by inserting the variable to the equation and verifying.Examples1. 5 45 y = 63 5(63)=y(45) 315=45y y=7
2. x+2 2 4 6 = x+2 (x+2)²=6(24) (x+2)²=144 x+2= +/- 12 x+2=+/- 12 x= 10 or -14
3. 16 x-1 x-1 = 4 16(4)=x²-2 64=x²-2 ∫66=∫x² ∫66=x
These 2 are related because they both involve ratios.
![Page 3: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/3.jpg)
SIMILAR POLYGONSPolygons are similar iff they have corresponding angles that are congruent and their corresponding side lengths are proportional.
Examples 1-3Determine weather the polygons are similar. If so, write the similarity ratio and a similarity statement.1.
2.
<P congruent <T, <Q congruent <U ,<R congruent <V, <S congruent <W
PQ = 12 = 3 PS = 4 = 2TU 16 4 TW 6 3
124
166
P
S
Q
R
U
V
T
W
A
CB
E
F
D2016
24
1812
15
AB = 20 = 4 BC = 24 = 4 AC = 16 = 4DE 15 3 EF 18 3 DF 12 3
<A congruent <D, <B congruent <E ,<C congruent <F
![Page 4: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/4.jpg)
3. EH = 30 = 2 EF = 90 = 2 AD 45 3 AB 135 3
135
45
90
30
A B
D CE F
H G
![Page 5: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/5.jpg)
The only thing that these does is that it helps determine how much something is enlarged or reduced.
SCALE FACTOR
Examples1. Multiply the vertices of the photo A B C D by 3/2.
B (0,4)
A (0,0)
C (3,4)
D (3,0)
A(0,0)A(0 [3/2], 0[3/2])A(0,0)B(0,4)B(0[3/2], 4[3/2])B(0,6)C(3,4)C(3[3/2], 4[3/2])C(4.5,6)D(3,0)C(3[3/2],0[3/2])D(4.5,0)
A(0,0)
B(0,6) C(4.5,6)
D(4.5,0)
![Page 6: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/6.jpg)
2.
A(0,0)A(0[1/2], 0[1/2])A(0,0)B(0,6)A(0[1/2], 6[1/2])B(0,3)C(4.5,6)C(4.5[1/2], 6[1/2])C(2.25,3)D(4.5,0)D(4.5[1/2], 0[1/2])D(2.25,0)
A(0,0)
B(0,6) C(4.5,6)
D(4.5,0)
A(0,0)
B(0,3) C(2.25,3)
D(2.25,0)
Multiply the vertices of the photo A B C D by 1/2.
![Page 7: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/7.jpg)
3. Multiply the vertices of the photo A B C D by 4/3. ROUND IF NEEDED
A(0,0)A(0[4/3], 0[4/3])A(0,0)B(0,8)B(0[4/3], 8[4/3])B(0,11)C(4,8)C(4[4/3], 8[4/3])C(5.3,11)D(4,0)D(4[4/3], 0[4/3])D(5.3,0)
A(0,0)
A(0,0)
B(0,8)C(4,8)
D(4,0)
B(0,11) C(5.3,11)
D(5.3,0)
![Page 8: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/8.jpg)
o Right Triangle Similarity if you draw an altitude from the vertex of the right angle of a right triangle, you form 3 similar right triangles.
o You do this by using ratios like shortest side/longest side of 2 similar triangles then you simplify.
o This is an important skill because if someday you want to cut a tree of your house you have got to know how long it is so it doesn't crushes you house.x
y
8
z
3
Examples Find all of the sides
1. x = 3 1.125 = y 3.2 = 3 3 8 y 9.125 1.125 z 8x=9 ∫y² = ∫10.27 3.375 = 3.2z x= 1.125 y=3.2 3.2 3.2 z=1.1
Indirect Measurement
![Page 9: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/9.jpg)
6 ft6 ft
30 ft
3. Find the height of the tower.
6 = 30 30= x6x = 9006 6X = 150 150 + 6 = Height= 156 ft
x
2. Find the height of the Ceiba.
8 ft 8 ft
x
45 ft
8 = 4545= x2025= 8x8 8253.125= x253.125+8= height =261.125 ft
![Page 10: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/10.jpg)
Perimeter and Area
o Area- first you have to simplify the fraction of both shapes after you have done that you square the fraction.
o Perimeter- first you find the perimeter of each shape with that you create a fraction of each perimeters then simplify.
6 4 312
17
24
14
6(4)=24 16 = 24(4)=16 24 3
3(2)+12(2)=301(2)+7(2)=1616 8 30 = 15
14(4)= 5624(24)=9656= 796 12
1.Sides40&2540/25 = 8/5(8/5)² = 64/25
2.Sides 30&1230/12=5/2(5/2) ²= 25/4
3.Sides 94&8694/86=47/43(47/43) ²= 2209/1849
![Page 11: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/11.jpg)
TRIGONOMETRIC RATIOSo Trigonometric= the study of triangleso Sin A= Opposite/Hypotenuseo Cos A= Adjacent/Hypotenuseo Tan A= Opposite/Adjacento Solving a triangle means finding all of the angles and all of the
sides.o These are useful to solve a right triangle because it helps you find
the angles and the sides .Examples
Write the ratio as a # and decimal rounded.R
ST
13
12
5Sin R= 12/13 ≈ 0.92Cos T= 5/13 ≈ 0.38Tan S= 5/12 ≈ 0.42
![Page 12: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/12.jpg)
100 m40⁰
Tan 40 = x__ 100100 (Tan 40) = x83.90
x
B
42⁰
x12
Sin 42 = x/1212(Sin 42)= x = 8.02
CA
B
24
257
Cos A= 24/25 ≈ 0.96Tan B= 24/7 ≈ 3.42Sin B= 24725 ≈ 0.96
x
y
z12.6 cm38⁰
Cos 38= 12.6/YZYZ= 12.6/Cos 38YZ= 15.99 cm
![Page 13: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/13.jpg)
ANGLE OF ELEVATION & ANGLE OF DEPRESSION
o Angle of Elevation is a straight line going horizontally and another line that’s ABOVE the horizontal pointing somewhere, which together form the angle.
o Angle of Depression is a straight line going horizontally and another line that’s BELLOW the horizontal pointing somewhere, which together form the angle.
Angle of Depression
Angle of Elevation
![Page 14: Maria Elisa Vanegas 9-5. A ratio is a comparison of 2 things it could be 2 values. Examples 1.A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3 2.](https://reader036.fdocuments.us/reader036/viewer/2022081602/551bd22a550346c3588b550c/html5/thumbnails/14.jpg)
Clasify each angle as angle of depression or elevation
ball
<1
<2<3
<41. <1 is angle of
elevation2. <2 is anlge of
depression3. <3 is angle of
elevation4. <4 is angle of
depression
5.
P
Ax
41⁰
Tan 41= 4000/xx= 4000/Tan 41x≈4601 ft
6.T
S Fx
7⁰
90 ft
Tan 7= 90/xx=90/Tan 7x≈ 733 ft