Transcript Lesson 4-6 - Elgin Local Schools

Lesson 9-2
The Area of a
Triangle
Objective:
Objective:
To find the area of a triangle given
the lengths of two sides and the
measure of the included angle.
By using right triangle trigonometry, we
can now make a few adjustments and
create many new formulas to help us
find specific information about triangles.
For instance, the area of a triangle
(k = ½ bh) is how we have known to
find the area of any triangle but most of
the time the height of a triangle is not
that easy to find. It had to be given to
us or we would have been in trouble.
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
In triangle ABC shown:
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
h
In triangle ABC shown: sinC =
a
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
h
In triangle ABC shown: sinC =
a
or
h = a (sinc)
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
So, by substitution:
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
So, by substitution:
1
k = absinC
2
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
The formula could be
also written as:
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
The formula could be
also written as:
1
1
k = acsin B or k = bcsin A
2
2
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
But in theory, what you need to realize is that to find
the area of a triangle all you need is two sides and
the included angle.
But, we can now use trigonometry to
make a few adjustments:
B
a
h
C
A
b
Because,
k = ½ (one side) (another side) (sine of included angle)
Two sides of a triangle have lengths of 7 cm
and 4 cm. The angle between the sides
measures 730. Find the area of the triangle.
The area of Δ PQR is 15. If p = 5 and
= 10, find all possible measures of < R.
q
Find the exact area of a regular hexagon
inscribed in a unit circle. Then approximate
the area to three significant digits.
Adjacent sides of a parallelogram have
lengths 12.5 cm and 8 cm. The measure of
the included angle is 400. Find the area of
the parallelogram to three significant digits.
Assignment:
Pgs. 342-343
1-19 odd,
18, 20, 22, 28, 30