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.

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Presentation transcript:

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: h A B C a b

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 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: h A B 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 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 Find the area of the parallelogram to three significant digits.

Assignment: Pgs odd, 18, 20, 22, 28, 30