Geometry
10.5 ‐ Trigonometry and Area
A. Today we are going to use trigonometric ratios to find missing pieces such as apothems and side lengths of regular polygons (rather than special right triangles)
Mar 11­7:07 AM
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B. Examples. Find the area of the following
1. Regular Pentagon with 6 cm sides
2. Regular Hexagon with side length 8 in
3. Regular Octagon with Perimeter 80 ft.
4. Regular Pentagon with radius 12 m.
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5. The radius of a garden in the shape of a regular pentagon is 18 ft. Find the area of the garden.
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C. Suppose you want to know the area of the Triangle ABC, but you only know m<A and side lengths b and c. You need to know the height to use A = ½bh. We can use trig to find it.
B
a
c
h
C
A
b
• Theorem 10 ‐ 8 (Area of a Triangle Given SAS): The area of a triangle is one half the product of the lengths of two sides and the sine of the included angle.
A = ½bc(sinA)
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D. Real‐World Examples
6. Two sides of a triangular building plot are 120 ft and 85 ft long. They include an angle of 85⁰. Find the area of the building plot to the nearest square foot.
7. A triangular park has two sides that measure 200 ft and 300 ft and form a 65⁰ angle. Find the area of the park to the nearest hundred square feet. Mar 11­7:13 AM
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10.5 homework page 561 numbers 1 ­ 3, 5, 6 ­ 10, 11 ­ 17
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Apr 22­11:02 AM
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Apr 22­11:07 AM
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Apr 22­11:12 AM
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