12$20Trigonometry

12$20Trigonometry - Geometry The three primary...

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Unformatted text preview: Geometry The three primary Trigonometric Ratios are Sine, Cosine, and Tangent. As we learned previously, triangles with the same angle measures have proportional sides. If you know one angle in a right triangle, you can use sin, cos, and tan to find the ratio of the lengths of its sides. Sine, Cosine, and Tangent Sin x o = Cos x o = Tan x o = 12.1 Trigonometry opposite hypotenuse adjacent hypotenuse opposite adjacent x o adjacent opposite h y p o t e n u s e Find sin x, cos x, and tan x in the right triangles below: 1. 2. Sin x o = Cos x o = Tan x o = x o 5cm 12cm 13cm 5 c m 3cm 4cm x o If you know an angle, you can use a calculator to find the ratios: 1. sin 34 o = 2. cos 55 o = 3. tan 18 o = Sin x o = Cos x o = Tan x o = Use a calculator to find the missing lengths below: 1. 2. 5cm x y 27 o 58 o 22cm b a Geometry12.1 Trigonometry You can use trigonometric inverses to find an angle based on a ratio: Sin, Cos, and Tan turn an angle into a ratio. Sin-1 , Cos-1 , and Tan-1 turn a ratio into an angle measure. Example: Find the measure of angle x in each triangle below: (make sure your calculator is set to degrees not radians) 1. 2. 5cm 12cm 13cm x o x o 109 in 60 in 9 1 i n Practice: Find the missing information in each right triangle below: (round to the hundredth) 1. 2. 3. x o 15cm 11cm x 5cm 35 o x 9cm 15 o Practice: Find the apothem in each regular polygon below: 1. 2. 3. Find the sides. 8cm 10cm 6cm Geometry Trigonometry Practice: Basics Name________________________ Period _____ Practice: Solve for x in each of the diagrams below. 1. 2. 3. 1. _____ 2. _____ 3. _____ Practice: Solve each. Round decimal answers to the tenth unless noted otherwise. 4. What is the measure of the smallest angle in a 20-21-29 right triangle? Round your answer to the tenth of a degree. 4. _____________ 5. A right triangle has a short leg measuring 10cm and one acute angle measure of 55 o . What is the length of the hypotenuse? 5. _____________ 6. What is the length of the apothem of a nonagon whose sides measure 4cm? 6. _____________ 7. Pentagon ABCDE has an edge length of 6cm. What is the length of segment AC? 7. _____________ 34 o x 4 c m 5cm 4cm x 77cm x 8 5 c m Geometry Practice: Solve each. Round decimal answers to the tenth unless noted otherwise. 8. What is the side length of a 12-gon whose apothem is 20cm long? 8. _____________ 9. Find the area of a 15-gon whose sides measure 2cm. 9. _____________ 10. A decagon of side length of 10cm contains an inscribed circle. What is the area of the inscribed circle in terms of tan and pi? ex. 2 ) 75 tan 3 ( 10. _____________ 11. What is the altitude h of the triangle below? 11. _____________ 12. A regular polygon has an apothem of about 101cm and a side length of 32 cm. How many sides does it have?...
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This note was uploaded on 10/31/2010 for the course TRI 198 taught by Professor Kbr during the Summer '10 term at Park.

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12$20Trigonometry - Geometry The three primary...

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