Chapter 9-Triangle Trigonometry

Solving Right Triangles

Area of a Triangle

Law of Cosines/Law of Sines

Trigonometry in Navigation and Surveying

Pythagorean Theorem: a^2+b^2=c^2 (only used with right triangles)

Triangle Sum Theorem: x+y+z=180 degrees

SohCahToa: sinθ=opposite/hypotonuse; cosθ=adjacent/hypotonuse; tanθ=opposite/adjacent

angle of elevation/depression

angle-of-elevation-image003

area of a triangle: A=(.5)bh=(.5)absinc

area of a segment: A=(.5)(r^2)θ - (.5)(r^2)(sinθ)

If S,C or T is capitalized it means that there is a restricted domain

Law of Sines: SinA/a=SinB/b=SinC/c

Law of Cosines: c^2=a^2+b^2-2abcosC

not unique is when there are multiple triangles that can be formed and unique is when only 1 triangle can be formed from the given measurements

not unique: <A=40,<B=50

unique: a=8, b=6, b=7

Use what is given in stroy problem to draw out a sketch

Bearings are measured from the North direction in the clockwise direction

when things are going directions such as northeast it creates a 45 degree angle