Chapter 13
#17
Opener/Notes
Opener:
#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
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 = 48º, B = 75º, C = 57º
TARGET GOAL:
The students will be able to find the
area of a triangle using Hero’s Formula.
NOTES:
D: SEMI-PERIMETER (s)
s=
1 a+b+c
2






Where a, b, and c are sides of a triangle.
Hero’s Formula
is used to find the area of a triangle
when given 3 sides.
A=
s( s−a ) s−b ( s−c )






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
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
Example One:
Now use “s” to find the area.
A=

2nd ans  2nd ans

−29.7

  2nd

ans
− 42.3

  2nd

ans
−38.4



Example One:
A = 552.32 feet2
**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 = s( s−a ) s−b ( s−c )






TARGET GOAL:
The students will be able to find the
area of a triangle using Hero’s Formula.
#17 Homework
Worksheet--Show all work!!
Due Tomorrow
Solutions are on line