Presentation on theme: "RIGHT TRIANGLES AND TRIGONOMETRY By Brianna Meikle."— Presentation transcript:
RIGHT TRIANGLES AND TRIGONOMETRY By Brianna Meikle
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.
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
Finding the Length of a Leg Let c=13² and b=5² 13²=5²+a² 169=25+ a² 144=a² a=12
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.
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
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.
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%