precalc basics (trig)

right triangles are made up of…

a right angle and two acute angles

sum of three right triangle angles

180 degrees

sides opposite of the acute angles are called…

legs

side opposite of the right angle is called the…

hypotenuse

pythagorean theorem

a²+b²=c²

what do symbols of the pythagorean theorem represent

a and b are legs, c is the hypotenuse

trigonometry

the relationship between the angle measurements and the side lengths

sin

opposite/hypotenuse

cos

adjacent/hypotonuse

tan

opposite/adjacent

special right triangles

30-60-90 and 45-45-90

30-60-90 triangle

two acute and led are 30 and 69 degrees and third angle is right angle (90 degrees). corresponding side lengths are 1:square root of 3:2

45-45-90 triangle

two acute angles measure 45 and 45 degrees and the third angle is the right angle (90). Their corresponding side lengths are in the ratio 1:1:square root of 2.

law of sines

related the lengths of two sides of a triangle to the signed of the angles opposite those sides (a/sin A = b/sin b = c/sin C)

law of cosines

related the lengths of the three sides of a triangle to the cosine of the angle opposite one of the sides (a²=b²+c²)