Chapter 6

Oblique trianges are triangles that aren't right.  They can be obtuse or acute.

A.  Law of Sines

Deriving:

1. SinA = h/b         SinB = h/a
2. h = b sinA          h = a sinB
3. b sinA = a sin B
4. (sinA)/a = (sinB)/b

Formula:

Example:

a = 7     b = 8     A = 30 degrees

1. 7/(sin30) = 8/(sinX)
2. 7 sinX = 8 sin30
3. 7 sinX = 4
4. sinX = 4/7
5. arcsin(4/7) = X
6. X = 34.85 degrees

To use the law of sines you must have at least an angle and its opposite side.

B. New Area of a Triangle Formula

Deriving:

1. A = 1/2 b h
2. A = 1/2 c h
3. A = 1/2 c (b sin A)
4. A = 1/2 bc sin A

This a side-angle-side triangle.

Formula:

Example:

b = 7     c = 9     A = 20 degrees

1. A = 1/2 x 7 x 9 x sin20
2. A ~ 10.77 inches squared