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Chapter 9-Triangle Trigonometry (Solving Right Triangles (SohCahToa:…
Chapter 9-Triangle Trigonometry
Solving Right Triangles
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
If S,C or T is capitalized it means that there is a restricted domain
angle of elevation/depression
Area of a Triangle
area of a triangle: A=(.5)bh=(.5)absinc
area of a segment: A=(.5)(r^2)θ - (.5)(r^2)(sinθ)
Law of Cosines/Law of Sines
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
Trigonometry in Navigation and Surveying
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
