Chapter 7 Flashcards
what is geometric mean
between 2 #’s is the sq. root of their product
geometric mean formula?
a/x = x/b (proportion)
geometric mean with altitude
AD/BD = BD/CD (use triangle)
what does the altitude stand for in GM?
it IS the geometric mean between the 2 segments of the hypotenuse
how to find GM using legs of the hypotenuse :
each leg is GM between the hypotenuse and segment of the hypotenuse adjacent to that leg
GM using legs of hypotenuse formula
AC/AB = AB/AD or AC/BC = BC/DC (triangles)
how to find x,y,z using Geometric Mean?
plug formulas in like (hypo/leg = leg/side
Which Theorem for right triangle: legs squared (a and b) = hypotenuse squared (c)
Pythagorean Theorem
how to determine if a triangle is right?
use Pythagorean Theorem
what is a pythagorean triple?
when 3 whole 3’s satisfy the equation a sq. + b sq. = c squared
for a 45-45-90(angles) triangle, how do you find the hypotenuse or legs?
H= L(square root of 2) L = 1/2 x H(square root of 2)
for a 30-60-90 triangle how do you find the hypotenuse or legs?
if you need the short leg: 1/2 x hypotenuse
if you need the long leg: 1/2 x H(square root of 3)
To find hypotenuse: LL formula = SLsquare root of 3
Angle of elevation or depression formula:
tan of angle = opposite/ adjacent
what is sin ratio
sin R = leg opposite angle R/ hypotenuse
cos ratio
cos R = leg adjacent to angle R/hypotenuse
