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JOURNAL 7,8

JOURNAL 7,8. A ratio is when you express two numbers that are compared by division. It can be shown in different ways: A:B A to B A/B. Examples :. The ratio of studentes per teacher is 4:1, 4 to 1, 4/1. The ratio of tennis studemts per court is 6:1, 6 to 1, 6/1.

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JOURNAL 7,8

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  1. JOURNAL 7,8

  2. A ratio is when you express two numbers that are compared by division. • It can be shown in different ways: A:B A to B A/B

  3. Examples: The ratio of studentes per teacheris 4:1, 4 to 1, 4/1. The ratio of tennisstudemts per courtis 6:1, 6 to 1, 6/1. The ratio of thepeeople in red per people in whiteis 53 to 4, 53:4, 53/4

  4. A proportion is an equation that states that two ratios are the same, equal. • How to solve a proportion: 1. First you have to cross multiply the numbers and the variable. After you are done multiplying, you have to leave 2. If the proportion involves an algebraic equation you first cross multiply, simplify by dividing, find the square roots of both sides and re write them as two equations and finally subtract two from both sides.

  5. Example 1: x/5 = 4/10 10x=20 /10 /10 x=2 2/5=2/5 Examples 2: 6/x = 3/8 3x=48 /3 /3 6/16=4/10 x=16 Examples 3: x/12 = 6/7 7x=72 /7 /7 10.3/12=6/7 x=10.3

  6. A ratio and a proportion are related because a proportion is an equation where 2 ratios are equal. Also because they depend on each other, if you want to make a proportion you need to have ratios. * If you want to make sure your proportion is equal you have to plug the answer to the variable and solve the proportion by cross multiplying and if both sides equal the same number then it is correct

  7. When two polygons are similar, it means that their corresponding angles are congruent and their corresponding side lengths are proportional. Examples: 2 2 8 8 5 5 10 10 1 8 X has tobe 4! x X has toequal 20! x 4 4 X has toequal 16! 16 5 16 x

  8. A scale factor describes how much a figure can be reduced or enlarged. A ratio of two corresponding lengths in two figures. d d a a 2 2 4 4 6 6 f g 20 2 20 e f b c 2 6 b c 10 The ratio of ab todfis 6:2 The ratio of bctoefis 10:2, 5:1

  9. d a 9 9 18 18 e f 7 b c 14 The ratio of actodfis 18:9, 2:1

  10. When using similar triangles to perform indirect measures you have to use proportions to find your answer. Use the actual height and the measure of shadows. • It is an important skill because with it, in real life you could find many measurments of things like builidings, houses and it helps in different jobs.

  11. Theboywantstoseehowhighhis houseisbecause he wantstoseeif he could climbitwithhisfriendssomeday. Theshadow of hishouseis 5. Hishightis 4.5 meters and hisshadowis 2. x 4.3 4.3 2 2 5/x = 4.3/2 4.3x=10 /4.3 /4.3 X=2.3 5 Thesameboyisverycurious and wantstoknowthehight of thestatue of libertybecuase he didntfindthatsort of information in histextbook. He knewthatthattheshadow of thestatuewas 20 and hishightwas 4.3 and hisshadowwas 2. x 20/x = 4.3/2 4.3x=40 X=9.3 20

  12. 33/x = 4.3/2 4.3x=66 X=15.3 4.3 x 2 33 Thesameboywenttoparis and wantedtoknowtheheight of theeifeltowersincehisparentsdidnttellhim. He heard in classthatitsshadowwas 33. he knewthathisheightwas 4.3 and hisshadowwas 2.

  13. How to use the scale factor to find the perimeter and area. • PERIMETER: To find the perimeter using scale factor, you first need to find the perimeter of each triangle. Then you create a fraction with each perimeter, but remember, it is the smaller shape over the bigger shape. Then you simplify the fraction. The ratio of the perimeter is the same as the ratio of their sides. • AREA: To find the area using scale factor, you first need to find the area of each shape. You make a fraction out of those areas (small shape over the bigger shape). After you have made the fraction, you simplify it all the way and then you square it.

  14. Perimeter: 12/24 = 1/2 10 4 5 Area: 12*2/48*2 = 1*2/4*2 8 3 4 6 6 4 4 Perimeter: 16/24 = 2/3 Area: 16*2/ 36*2 = 4*2/ 9*2 6 4 6 3 3 6 6 6 Perimeter: 8/17 Area: 2.5*2/13.75*2 2 5

  15. The three trigonometric ratios • Sin=Opposite/Hypotenuse • Cos=Adjacent side/Hypotenuse • Tan=Opposite side/Adjacent • To solve a triangle is to find all the sides and angles of a triangle.

  16. Sin: 7/9 Cos: 5/9 Tan: 7/5 Sin: 8/12 Cos: 6/12 Tan: 8/6 8 12 9 7 6 5 Sin: 5/15 Cos: 13/15 Tan: 5/13 15 5 13

  17. How are they used to solve for right triangles? • To find the angles: 1. you need to know what type of ratio it is. 2.Then you plug in the the inverse of the ratio into your calculator (Ex. Sin-1(12/13) = 66.92) • To find the sides: 1.To find the side, you need to find the type of ratio. 2.Then, you make a proportions with the missing value and the other side. 3.You plug in the side measure and then the ratio with the angle measure between those sides. (Ex. Tan40 = X; 100(tan40) = 83.9

  18. Sin42: x/12 12(sin42)=x X= 8.02 12 x 42 Sin(12/13) Sin-1(12/13) X = 67.38 13 x 12 8 x Sin42 = 8/x 8 = xSin42/sin42 X = 11.96 42

  19. Angles of Elevation and Depression • Angle of Elevation: it is the angle formed by a horizontal line and a line of sight to a point above the line. Watch from down to up. • Angle of Depression: the angle formed by a horizontal line and a line of sight into a point below the line. Watch from up to down.

  20. Angle of elevation Angle of depression

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