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JOURNAL 7 & 8

JOURNAL 7 & 8. Maria Elisa Vanegas 9-5. RATIO. A ratio is a comparison of 2 things it could be 2 values. Examples A(-2,-1) B(4,3) rise 3-(-1) 4 2 run = 4-(-2) = 6 = 3. 3. A(-2,-2) B(2,2) rise -2-2 - 4 1 run = -2-2 = -4 = . 2. A(-1,3) B(1,4) rise 3-4 - 1 1

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JOURNAL 7 & 8

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  1. JOURNAL 7 & 8 Maria Elisa Vanegas 9-5

  2. RATIO A ratio is a comparison of 2 things it could be 2 values. Examples A(-2,-1) B(4,3) rise 3-(-1)42 run = 4-(-2) = 6 = 3 3. A(-2,-2) B(2,2) rise -2-2 -41 run = -2-2 = -4 = 2. A(-1,3) B(1,4) rise 3-4 -11 run = -1-1 = -2 = 2 PROPORTION A 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. Examples 545 y = 63 5(63)=y(45) 315=45y y=7 2. x+22 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.

  3. Similar Polygons Polygons are similar iff they have corresponding angles that are congruent and their corresponding side lengths are proportional. Examples 1-3 Determine weather the polygons are similar. If so, write the similarity ratio and a similarity statement. 1. 2. T W U V 16 <P congruent <T, <Q congruent <U ,<R congruent <V, <S congruent <W 6 P S PQ= 12 = 3 PS = 4 = 2 TU 16 4 TW 6 3 Q R 4 12 A E 15 <A congruent <D, <B congruent <E ,<C congruent <F D 18 20 16 12 AB= 20 = 4BC = 24 = 4AC = 16 = 4 DE 15 3 EF 18 3 DF 12 3 F B 24 C

  4. 3. EH = 30 = 2EF = 90 = 2 AD 45 3 AB 135 3 135 A B D C 45 90 E F H G 30

  5. SCALE FACTOR The only thing that these does is that it helps determine how much something is enlarged or reduced. Examples 1. Multiply the vertices of the photo A B C D by 3/2. C(4.5,6) B(0,6) C (3,4) B (0,4) A (0,0) 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) D(4.5,0)

  6. 2. Multiply the vertices of the photo A B C D by 1/2. C(4.5,6) B(0,6) B(0,3) C(2.25,3) A(0,0) D(2.25,0) D(4.5,0) A(0,0) 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)

  7. 3. Multiply the vertices of the photo A B C D by 4/3. ROUND IF NEEDED B(0,11) C(5.3,11) C(4,8) B(0,8) A(0,0) D(4,0) A(0,0) D(5.3,0) 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)

  8. Indirect Measurement • 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. • You do this by using ratios like shortest side/longest side of 2 similar triangles then you simplify. • 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 Examples Find all of the sides y 3 x = 31.125 = 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 8 z

  9. 3. Find the height of the tower. 2. Find the height of the Ceiba. x x 30 ft 45 ft 6 ft 6 ft 8 ft 8 ft 6 = 30 30= x 6x = 900 6 X = 150 150 + 6 = Height= 156 ft 8 = 45 45= x 2025= 8x 8 253.125= x 253.125+8= height =261.125 ft

  10. Perimeter and Area 24 12 6 4 3 14 • Perimeter- first you find the perimeter of each shape with that you create a fraction of each perimeters then simplify. 7 1 14(4)= 56 24(24)=96 56= 7 96 12 6(4)=24 16 = 2 4(4)=16 24 3 3(2)+12(2)=30 1(2)+7(2)=16 16 8 30 = 15 • Area- first you have to simplify the fraction of both shapes after you have done that you square the fraction. 3. Sides 94&86 94/86=47/43 (47/43) ²= 2209/1849 2. Sides 30&12 30/12=5/2 (5/2)²= 25/4 1. Sides40&25 40/25 = 8/5 (8/5)² = 64/25

  11. Trigonometric ratios • Trigonometric= the study of triangles • Sin A= Opposite/Hypotenuse • Cos A= Adjacent/Hypotenuse • Tan A= Opposite/Adjacent • Solving a triangle means finding all of the angles and all of the sides. • These are useful to solve a right triangle because it helps you find the angles and the sides . Examples Writethe ratio as a # and decimal rounded. R Sin R= 12/13 ≈ 0.92 Cos T= 5/13 ≈ 0.38 Tan S= 5/12 ≈ 0.42 13 5 S 12 T

  12. Tan 40 = x__ 100 100 (Tan 40) = x 83.90 Sin 42 = x/12 12(Sin 42)= x = 8.02 B 12 x x 40⁰ 42⁰ 100 m 12.6 cm z C x 24 38⁰ A 7 25 Cos 38= 12.6/YZ YZ= 12.6/Cos 38 YZ= 15.99 cm y Cos A= 24/25 ≈ 0.96 Tan B= 24/7 ≈ 3.42 Sin B= 24725 ≈ 0.96 B

  13. Angle of Elevation & Angle of Depression • Angle of Elevation is a straight line going horizontally and another line that’s ABOVE the horizontal pointing somewhere, which together form the angle. • Angle of Depression is a straight line going horizontally and another line that’s BELLOWthe horizontal pointing somewhere, which together form the angle. Angle of Depression Angle of Elevation

  14. Clasify each angle as angle of depression or elevation <1 isangle of elevation <2 isanlge of depression <3 isangle of elevation <4 isangle of depression <4 <3 <2 <1 ball P T 6. 7⁰ Tan 41= 4000/x x= 4000/Tan 41 x≈4601 ft 5. Tan 7= 90/x x=90/Tan 7 x≈ 733 ft 90 ft S F x 41⁰ A x

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