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Lesson 9-2Lesson 9-2
The Area of a The Area of a TriangleTriangle
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Objective:Objective:
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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.
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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.
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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.
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But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
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But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
In triangle ABC shown:
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But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
In triangle ABC shown:
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But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
In triangle ABC shown: or
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But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
So, by substitution:
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But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
So, by substitution:
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But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
The formula could be also written as:
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But, we can now use trigonometry to make a few adjustments:
h
A
B
C
a
b
The formula could be also written as:
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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.
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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)
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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.
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The area of Δ PQR is 15. If p = 5 and q = 10, find all possible measures of < R.
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Find the exact area of a regular hexagon inscribed in a unit circle. Then approximate the area to three significant digits.
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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.
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Assignment:Assignment:
Pgs. 342-343 Pgs. 342-343 1-19 odd, 1-19 odd,
18, 20, 22, 28, 3018, 20, 22, 28, 30