for a right angle triangle with legs a, b. and hypotenuse. c=a2+b2
the square of the hypotenuse is equal to the sum of the squares legs
Useful when building structures
the Pythagorean theory states that in a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the legs
to find the hypotenuse:
Hypotenuse
the opposite of the right angle
the longest side of a right angle triangle. In this image, the hypotenuse is written in blue.
Opposite side
the side that does not form one of the arms of the angle being considered. The opposite side in this triangle is written in red
Cosine
Sine
the sine of an angle is the length of the opposite, divided by the length of the hypotenuse
Tangent
in any right riangle, the cosine of an angle is the length of the adjacent, divided by the length of the hypotenuse
the tangent is the length of the opposite side, divided by the length of the adjacent side
Linear Relations
the rate of change is represented by the sloe of the line
linear relations is a relation between two variables as a straight line when graphed
a coefficient is a number that is multiplied by a variable -in y=3x, the coefficient of x is 3
calculating the slope for the given equation:
the formula for finding the slope in a graph is rise/run
rise=2
run=4
rise/run = 2/4
therefore, the slope in this is graph is 0.5
horizontal & vertical lines: - a horizontal line has a slope of 0 - a vertical line has a slope that is undefined
Linear Equations
opposite operations: -opposite operations are operations that "undo" each other -addition and subtraction are opposite operations -multiplication & division are opposite operations
the side that forms one of the angle being considered, but is not the hypotenuse. The adjacent side in triangle is highlighted green
Adjacent
to solve a linear equation involving fractions: to solve for the equation -6=x/5, you will first need to get x by itself by cancelling out the 5 in the denominator of the fraction by multiplying. Next on the left side you multiply 5x(-6) which is -30, therefore, x=-30
to rearrange an equation from standard from into linear slope-intercept form:
in the formula y=mx+b, m is the slope of the line, x is the variable and b is the y-intercept
Linear Systems
Chapter 3,4 and 5
point of intersection
a set of 2 or more linear equations that are considered at the same time
the point at which two lines cross
there are 3 versions of the slope formula: 1. Slope intercept: y=mx+b 2. Point slope: y-y1=m(x-x1) 3. Standard: Ax+By=C
using the substitution method to solve a linear equation:
using the elimination method to solve a linear equation
