think back to geometry. write down the ways to prove that two triangles are congruent
TRANSCRIPT
Think back to geometry. Write down the ways to prove that two triangles are congruent.
Warm-Up: May 20, 2013
The Law of SinesSection 6.1
For a triangle with angle measures A, B, C and side lengths opposite those angles of a, b, c:
True for any triangle (acute, right, obtuse)
The Law of Sines
C
c
B
b
A
a
sinsinsin
c
C
b
B
a
A sinsinsin
Solving a triangle means finding all side lengths and angle measures
Use Law of Sines A+B+C=180˚ For examples, you-try’s and homework,
round side lengths and angle measures to 3 decimal places.
Law of Sines can be used to solve a triangle if 2 angles and 1 side are known (SAA or ASA) or two sides and an angle opposite one of them (SSA)
Solving a Triangle
1. Start by drawing a rough sketch of a triangle (not to scale)
2. Find the third angle measure (A+B+C=180˚)
3. Use Law of Sines twice to find the two missing side lengths
4. Draw a better version of your triangle (to scale)
5. Check that your longest side is across from biggest angle, shortest side is across from smallest angle
Solving a Triangle: SAA or ASA
Solve the triangle
Example 1: SAA
24
56
22
C
B
A
c
b
a
Solve the triangle
You-Try #1: SAA
82
64
14
C
B
A
c
b
a
Solve the triangle
Example 2: ASA
C
B
A
c
b
a
35
85
30
Solve the triangle
You-Try #2: ASA
5.22
40
12
C
B
A
c
b
a
Page 607 #1-13 Every Other Odd Page 608 #17-29 Every Other Odd Page 608 #33-45 Every Other Odd
Assignments
Find all angles θ in the interval [0, 2π) such that
Warm-Up: May 21, 2013
2
1sin
Homework Questions?
SSA: The Ambiguous Case Given two side lengths and an angle
opposite one of them, there could be 0, 1, or 2 triangles
Assume a, b, and A are given If , then there are no triangles If , then there is one right triangle If , then there are two
triangles If , then there is one triangle
The Law of Sines will give you the number of triangles
SSA: How Many Triangles?
Aba sinAba sin
baAb sinba
Solve the triangle
Example 3: SSA
C
B
A
c
b
a
20
40
30
Solve the triangle
Example 4: SSA
C
B
A
c
b
a
50
20
30
Solve the triangle
Example 5: SSA
C
B
A
c
b
a
150
30
10
Solve the triangle
You-Try #5: SSA
C
B
A
c
b
a
35
16
12
Page 607 #1-13 Every Other Odd Page 608 #17-29 Every Other Odd Page 608 #33-45 Every Other Odd
Assignments
Solve the triangle (hint: there are two solutions)
Warm-Up: May 22, 2013
C
B
A
c
b
a
28
13
8
Homework Questions?
An oblique triangle is one that does not contain a right angle
Area is one half the product of the length of two sides and the sine of the included angle
Area of an Oblique Triangle
CabArea
BacArea
AbcArea
sin2
1
sin2
1
sin2
1
Find the area of a triangle with the following measurements
Example 6: Area
22
50
20
A
feetc
feetb
Find the area of a triangle with the following measurements
You-Try #6: Area
125
5
8
B
yardsc
yardsa
Page 607 #1-13 Every Other Odd Page 608 #17-29 Every Other Odd Page 608 #33-45 Every Other Odd
Assignments