Measurement & Trigonometry
Solving Proportions
x/15 = 1/5
5x = 15
x =3
x/18 = 3/15
15x = 18 (3)
15x = 54
15x/15 = 54/15
x = 3.6
Rounding
Round to the nearest degree
43.66*
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 is 44*
4.87
0.87 is closer to 0.9 than 0.8, so 4.87 rounded to one decimal place is 4.9
4.87 rounded to one decimal place is 4.9
Key Terms
Hypotenuse
Tangent Ratio
Legs
Trigonometry
Cosine Ratio
Sine Ratio
Trigonometry - triangle measurement
Used to calculate lengths of sides and measures of angles in triangles
Sine Ratio = SinA o/h
Length of side opposite
Length of hypotenuse
Defining The Trigonometric Ratios
Hypotenuse
Opposite
Adjacent
CosA = a/h
Length of adjacent
Length of hypotenuse
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
tangent ratio:
tangent ratio are the ratio of a side opposite to the side adjacent the angle they represent
Legs Meaning:
refers to a side other than the one opposite the right angle. legs are also known as catenin.
Trigonometry Meaning:
the study of measurement of three-sided figures. trigonometry is the study of the measurement of the sides and angle in triangles
Cosine Ratio Meaning:
the length of the side adjacent to the angle divided by the length of the hypotenuse of the triangle
Sine Ratio Meaning:
the length of the opposite side divided by the length of the hypotenuse
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
Rectangle sides: 1.58 x 2 = 3.16 x 2 = 6.32
React Bottom: 2 x 1 = 2
Triangle: (1 x 1.5) / 2 = .75 x 2 = 1.5
Total: 6.63 + 2 + 1.5 = 9.82m2
Metric System meaning:
system of measurement that uses the meter, liter and gram as base unties of length, capacity, and weight respectively
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
Proportional Meaning:
two varying quantities are said to be in a relation of proportionality, multiplicatively connected to a constant
Key Terms
Proportional
Metric System
Imperial System
Corresponding Sides
Ratio
Similar Triangles
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
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
Fraction And Number Sense
Order the fraction in each set from least to greatest
3/8,5/32,1/2,3/4
3/8 = 12/32
1/2 = 16/32
3/4 = 24/32
Therefore from least to greatest they are 5/32, 3/8, 1/2, 3/4
3/8 + 3/16
6/16 + 3/16
9/16
Similar Triangles meaning:
Two triangles are similar if the only difference is size and possibly the need to turn or flip one around.
Ratio And Proportion
Write each ratio in simples form
54:18
54 divide by 18 = 3
18 divide by 18 = 1
54 divide by 18 = 3:1
x/3 = 1/5
5x = 3
x= 3/5