unit 8: right triangles & trigonometry Flashcards
isosceles right triangle theorem
in a 45-45-90 right triangle, the hypotenuse is √2 when legs are x
30-60-90 triangle theorem
in a 30-60-90 triangle, the shortest leg is x, the second shortest is x√3, and the longest is 2x
sin=
opposite/hypotenuse
cos=
adjacent/hypotenuse
tan=
opposite/adjacent
soh cah toa solves for ____
inverses solve for _____
sides
angles
right triangle similarity theorem
if an altitude is drawn to the hypotenuse of a right triangle, then the 2 triangles formed are similar to the original triangle and each other
geometric mean
√ab
geometric mean altitude theorem
an altitude is drawn to the hypotenuse of a right triangle has a length that is the geometric mean of the segments composing of the hypotenuse
geometric mean leg theorem
when an altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse adjacent to the leg
pythagorean theorem
a^2 + b^2 = c^2
pythagorean theorem converse
if a^2 + b^2 = c^2, then the triangle is a right triangle
pythagorean inequalities
a^2 + b^2 < c^2 it is obtuse
a^2 + b^2 > c^2 it is acute
law of sines
sinA/a = sinb=B/b = sinC/c
law of cosines
a^2 = b^2 + c^2 - 2bc(cosA), swap letters etc.
