Post on 22-Dec-2015
Lesson 9-2Lesson 9-2
The Area of a The Area of a TriangleTriangle
Objective:Objective:
Objective:Objective:
To find the area of a triangle given To find the area of a triangle given the lengths of two sides and the the lengths of two sides and the measure of the included angle.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:
h
A
B
C
a
b
But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
In triangle ABC shown:
But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
In triangle ABC shown:
But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
In triangle ABC shown: or
But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
So, by substitution:
But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
So, by substitution:
But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
The formula could be also written as:
But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
The formula could be also written as:
But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
bBut 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:
h
A
B
C
a
bBecause, 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 q = 10, find all possible measures of < R.
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:Assignment:
Pgs. 342-343 Pgs. 342-343 1-19 odd, 1-19 odd,
18, 20, 22, 28, 3018, 20, 22, 28, 30