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RIGHT TRIANGLES AND TRIGONOMETRY By Brianna Meikle

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The Pythagorean Theorem Pythagorean Theorem: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. o c²=a²+b² c is always the hypotenuse or the diagonal, while a and b are the legs.

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Finding the Length of a Hypotenuse (hypotenuse)²=(leg)²+(leg)² x²=3²+4² x²=9+16 x²=25 x=5 Pythagorean Theorem Substitute Multiply Add Find the positive square root Example of finding HypotenuseWhat you’re doing

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Finding the Length of a Leg Let c=13² and b=5² 13²=5²+a² 169=25+ a² 144=a² a=12

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Theorems About Special Right Triangles 45°-45°-90° Triangle Theorem In a 45°-45°-90° triangle, the hypotenuse is √2 times as long as each leg. 30°-60°-90° Triangle Theorem In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg.

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Finding a leg in a 45-45-90 triangle and the side lengths in a 30-60-90 triangle. Finding a leg in a 45-45- 90 Triangle Longer Leg in a 30-60- 90 Triangle What to do: 45-45-90 Triangle Theorem 30-60-90 Triangle Theorem Substitute Divide each side by √2.Divide each side by √3. Simplify * Numerator and Denominator by √2. *Numerator and Denominator by √3. Simplify

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Finding Trigonometric Ratios S.O.H.C.A.H.T.O.A. These letters stand for: Sine, Cosine, and Tangent To find the sine A: Use the Opposite Side over the Hypotenuse. To find the cosine A: Use the Adjacent Side over the Hypotenuse. To find the tangent A: Use the Opposite Side over the Adjacent Side.

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Learning the sine, cosine, and tangent will give you the ability to find the lengths of triangles. What is the necessity for the sine, cosine, and tangent?

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How well did Students Understand this chapter? What percentage of the time did students understand Chapter Nine? This year or past years Student #190% Student #2100% Student #340% Student #430% Student #595%

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