# RIGHT TRIANGLES AND TRIGONOMETRY By Brianna Meikle.

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Right Triangles and TrigonometryBy Brianna Meikle

The Pythagorean TheoremPythagorean 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. c=a+bc is always the hypotenuse or the diagonal, while a and b are the legs.

Finding the Length of a Hypotenuse (hypotenuse)=(leg)+(leg)x=3+4x=9+16x=25x=5

Pythagorean TheoremSubstituteMultiplyAddFind the positive square rootExample of finding HypotenuseWhat youre doing

Finding the Length of a Leg Let c=13 and b=513=5+a169=25+ a144=aa=12

Theorems About Special Right Triangles45-45-90 Triangle TheoremIn a 45-45-90 triangle, the hypotenuse is 2 times as long as each leg.

30-60-90 Triangle TheoremIn 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.

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 TriangleLonger Leg in a 30-60-90 TriangleWhat to do:45-45-90 Triangle Theorem30-60-90 Triangle TheoremSubstituteSubstituteDivide each side by 2.Divide each side by 3.SimplifySimplify* Numerator and Denominator by 2.*Numerator and Denominator by 3.SimplifySimplify

Finding Trigonometric RatiosS.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.

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?

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%