Download WarmUp: 1) Find the values of the six trigonometric functions for

Warm­Up:
1) Find the values of the six trigonometric functions for angle θ.
A
θ
c
b
C
o
o
a
B
2) Solve ΔABC if A = 15 , C = 90 , and b = 8. Round measures of sides to the nearest tenth, and measures of angles to the nearest degree.
Section 13­4: Law of Sines
Write a formula for the area of the triangle below.
A
c
B
b
h
a
C
Suppose we dont know the height. What is a different expression representing the height? (Hint: Use the sine function).
What is a new equation for the area of this triangle?
Area Formula for a Triangle:
A = 1 bc sin A
2
A = 1 ac sin B
2
A = 1 ab sin C
2
A
b
c
B
a
C
Examples:
1) Find the area of ΔABC to the nearest tenth.
A
6 cm
C
All three area formulas represent the same area, so
1 bc sin A = 1 ac sin B = 1 ab sin C
2
2
2
Divide all three sides by 1/2 abc, what is left?
o
25
B
3 cm
The Law of Sines:
In ΔABC, the ratio between the sine of any angle and its opposite side to the ratio between the sine of any other angle and its opposite side.
sin A = sin B = sin C a
b c
C
Examples:
2) Solve ΔABC.
a
B
100
o
9
53 o
c
A
Homework: pg. 790­791 #12­22 even, 32, 34, 40, 41
Section 13­4 Vocab