Measurement & Trigonometry

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Measurement & Trigonometry

1km = 1000m 1m = 100cm 1m = 1000m 1cm = 10 mm 1 tonnage = 1000kg 1kg = 1000g 1 liter = 1000m 1m3 = 1000 liter 1cm3 = 1ml

Ratio And Proportion

x/3 = 1/5

x= 3/5

5x = 3

54:18

54 divide by 18 = 3

54 divide by 18 = 3:1

18 divide by 18 = 1

Write each ratio in simples form

Similar Triangles meaning: Two triangles are similar if the only difference is size and possibly the need to turn or flip one around.

Fraction And Number Sense

3/8 + 3/16

9/16

6/16 + 3/16

Therefore from least to greatest they are 5/32, 3/8, 1/2, 3/4

3/8,5/32,1/2,3/4

3/4 = 24/32

3/8 = 12/32

1/2 = 16/32

Order the fraction in each set from least to greatest

Corresponding Sides Meaning: touch the same two angle pairs, when the sides are corresponding it means to go from one triangle to another. you can multiply each side by the same number

Ratio Meaning: ratio indicates how many times one number contains another. ex; the ratio if lemons to orange's is 6:8 or 3:4 and the ratio of orange's to the total amount of fruit is 8:14 or 4:7

Ratio

Similar Triangles

Imperial System

Corresponding Sides

Proportional

Metric System

Proportional Meaning: two varying quantities are said to be in a relation of proportionality, multiplicatively connected to a constant

Imperial System meaning: a system of weights and measures similar but not always the same. Ex; of imperial measures, length, inches, feet, yards, area, square feet, acres

Metric System meaning: system of measurement that uses the meter, liter and gram as base unties of length, capacity, and weight respectively

Determine if 980cm2 of waterproof cancans will be enough to build a pup tent (triangular prism) with the following dimensions length of 2m, width of 1m and height of 1.5m

Total: 6.63 + 2 + 1.5 = 9.82m2

Rectangle sides: 1.58 x 2 = 3.16 x 2 = 6.32

Triangle: (1 x 1.5) / 2 = .75 x 2 = 1.5

React Bottom: 2 x 1 = 2

Sine Ratio Meaning: the length of the opposite side divided by the length of the hypotenuse

Cosine Ratio Meaning: the length of the side adjacent to the angle divided by the length of the hypotenuse of the triangle

Trigonometry Meaning: the study of measurement of three-sided figures. trigonometry is the study of the measurement of the sides and angle in triangles

Legs Meaning: refers to a side other than the one opposite the right angle. legs are also known as catenin.

tangent ratio: tangent ratio are the ratio of a side opposite to the side adjacent the angle they represent

Hypotenuse Meaning: in a right triangle the hypotenuse is the longest side, an opposite side is the one across from a given angle and a adjacent side is next to a given angle

CosA = a/h

Length of adjacent Length of hypotenuse

Defining The Trigonometric Ratios

Adjacent

Opposite

Sine Ratio = SinA o/h

Length of side opposite Length of hypotenuse

Trigonometry - triangle measurement

Used to calculate lengths of sides and measures of angles in triangles

Key Terms

Cosine Ratio

Sine Ratio

Legs

Trigonometry

Hypotenuse

Tangent Ratio

Rounding

4.87 rounded to one decimal place is 4.9

4.87

0.87 is closer to 0.9 than 0.8, so 4.87 rounded to one decimal place is 4.9

43.66* round to the nearest degree is 44*

0.66 is closer to 1 than to 0, so 43.66* round to the nearest degree is 44*

43.66*

Round to the nearest degree

Solving Proportions

x = 3.6

15x = 54

15x/15 = 54/15

x/18 = 3/15

15x = 18 (3)

x/15 = 1/5

x =3

5x = 15