Triangles & Vectors (4.7, 8.1, 8.2)

sin A/a = sin B/b

Law of Sines

sin (A) < a/b

N.S. for Ambiguity Case

sin (A) = a/b

One Solution for Ambiguity Case

sin (A) > a/b

Two solutions for Ambiguity Case

Subtract angle B from 180 to get angle B2; Subtract angle B2 and A from 180 to get C2; use law of sines to get c2 from C2.

How to solve a two solution ambiguity case triangle.

<x2-x1, y2-y1>

Component form for vectors

√(component x²) + (component y²)

Magnitude for vectors

tan-1 = y/x

Directional Angle for vectors

Directional angle

Angle from the positive x-axis (vector); typical angle.

Quadrant Bearing angle

Angle from the north-south lines ‘compass’ reading (SHIP)

True Bearing angle

Angle clockwise from the North; “heading” reading (PLANE)

Distribute the magnitude (mph or wtv) to the cos & sin of the angle in directional form; add all of those to get component; find magnitude; use directional angle to find angle.

How to solve vector applications.

a² = b² + c²-2bc(cosA)

Law of Cosines

Area= ½ (bc(sinA))

Area formula for 2 sides & their included angle

s = ½ (a+b+c); Area = √s(s-a)(s-b)(s-c)

Area given 3 sides (Heron’s Formula)