Download no.17 ch13.HAA slides

Opener:
Chapter 13
#17
Opener/Notes
Opener:
#2
Use the Law of Cosines to solve the
triangle to the nearest degree given that
a = 16.4, b = 21.1, and c = 18.5.
A = 48.4º, B = 74.1º, C = 57.5º
#1
List the 3 formulas for the Law of
Cosines.
a2 =b2 +c2 !2bc cosA
b2 =a2 +c2 !2ac cosB
c2 =a2 +b2 !2ab cosC
TARGET GOAL:
The students will be able to find the
area of a triangle using Hero’s Formula.
NOTES:
Hero’s Formula
is used to find the area of a triangle
when given 3 sides.
D: SEMI-PERIMETER (s)
s=
1 a+b+c
2
"
$
#
%
'
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Where a, b, and c are sides of a triangle.
Example One:
Find the area of the triangle having sides
of lengths a = 29.7 feet, b = 42.3 feet, and
c = 38.4 feet.
Find the semi-perimeter first.
s= 29.7+42.3+ 38.4
2
A=
s( s!a ) s!b ( s!c )
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Note: Use “2nd ans” and round last!
Example One:
Find the area of the triangle having sides
of lengths a = 29.7 feet, b = 42.3 feet, and
c = 38.4 feet.
Find the semi-perimeter first.
s= 29.7+42.3+ 38.4
2
s = 55.2
A=
Example One:
Example One:
Now use “s” to find the area.
A = 552.32 feet2
"
2nd ans $ 2nd ans
#
!29.7
%"
' $ 2nd
&#
ans
! 42.3
%"
' $ 2nd
&#
ans
!38.4
%
'
&
**Remember to Round Last**
Example Two:
Application
Lauren plans to paint a triangular wall in her Aframe cabin. Two sides measure 7m each, and
the third side measures 6m. How much paint
will she need to buy if a can of paint covers 7.5
square meters.
Solve this with your group.
Show all work.
• Draw a picture
• Define the variable
• Set up an equation
• Solve
• Answer the problem
Example Two:
s = 10
A = 18.97
She needs 3 cans of paint.
Summary of Area of a
Triangle:
h
Base
b
Area= 1 SinAcb
2
c
A
b
a
c
A= 1 bh
2
A=
TARGET GOAL:
The students will be able to find the
area of a triangle using Hero’s Formula.
s( s!a ) s!b ( s!c )
"
$
#
%
'
&
1. Take out a sheet of paper.
#17 Homework
Worksheet--Show all work!!
Due Tomorrow
Solutions are on line
2. On the top half of the paper, draw an
x-y axis and the unit circle.
3. Lable all quadrantal angles, all 45º
angles, all 60º angles, and all 30º angles
in all quadrants in both degrees and
radians. (You will need to do this on the
NO calculator part of the test.)
4. Put in the correct ordered pairs for the
unit circle on the x and y axis.
1. Sketch each of the following angles.
2. Lable the reference angle.
1. Take out your red pen and your foldable.
3. Put the correct proportions for the sides
2. Make corrections in red pen.
of the triangle.
(
1. Take out your red pen.
2. Make corrections in red pen.
a)
23)
6
b)
390º
c)
!11)
3
d)
!405º
e)
! 5)
4
f)
540º