Geometry 9.5 Trigonometric Ratios May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator2 Goals I can find the sine, cosine, and tangent of an acute.

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Presentation transcript:

Geometry 9.5 Trigonometric Ratios

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator2 Goals I can find the sine, cosine, and tangent of an acute angle. I can solve problems using trigonometric ratios.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator3 Terminology No one, uses the word trigonometry. It’s

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator4 What is trig? Literally, the measure of triangles. An extremely useful, practical and powerful math tool. A branch of math that finds its way into practically everything we do. Usually learned in high school.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator5 What you will learn… The basic terms and methods of solving right triangles. How to solve problems using trig.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator6 Trig Ratios Based on the sides of a right triangle. We will study only three: Sine Cosine Tangent

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator7 Right Triangle Hypotenuse Leg A From  A, this leg is the Adjacent side. From  A, this leg is the Opposite side.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator8 Right Triangle Hypotenuse Leg A From  A, this leg is the Adjacent side. From  A, this leg is the Opposite side. B From  B, this leg is the Adjacent side. From  B, this leg is the Opposite side.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator9 Right Triangle Hypotenuse Adjacent Opposite A

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator10 Trig Ratio Definition: Sine Hypotenuse Adjacent Opposite A Sine of  A = Opposite Hypotenuse

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator11 Trig Ratio Definition: Cosine Hypotenuse Adjacent Opposite A Cosine of  A = Adjacent Hypotenuse

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator12 Trig Ratio Definition: Tangent Hypotenuse Adjacent Opposite A Tangent of  A = Opposite Adjacent

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator13 Abbreviations Tangent of  A = Opposite Adjacent Sine of  A = Opposite Hypotenuse Cosine of  A = Adjacent Hypotenuse sin A cos A tan A

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator14 Memory Aid Sine is Opposite over Hypotenuse. Cosine is Adjacent over Hypotenuse. Tangent is Opposite over Adjacent. SOHCAHTOA

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator15 Writing RatiosSOHCAHTOA A B ? ? ? ? ? ? ? ? ? ? ? ?

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator16 Find these values using your calculator—Make sure you’re in Degree Mode!!! SIN 15 COS 45 TAN 45 COS 80 SIN 10 TAN 5 COS 60 SIN

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator17 Solving Triangles Carefully analyze what given information you have. Decide what you are trying to find. Ask: how do you use the given information to solve the problem? WRITE AN EQUATION. (SOHCAHTOA) Solve.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator18 Example 1Find x. 28  x 15 From the 28  angle, x is the ? Opposite side, and 15 is the Hypotenuse. What trig ratio is this? Sine (SOHCAHTOA)

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator19 Example 1Find x. 28  x 15 Write the equation and solve.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator20 Example 2Find y. 31  y 56 Write the equation and solve.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator21 Example 3Find a. 40  a 8 Write the equation and solve.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator22 Algebra Reminder Solve:

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator23 Example 4Find a. 40  a 17 Write the equation and solve.

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator24 Example 5Find x & y. 78  xy 150

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator25 Angle of Elevation Horizontal Angle of Elevation

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator26 Angle of Depression Horizontal Angle of Depression

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator27 Problem 30 yd 15  h Standing 30 yards from a tree, the angle of elevation to the top of the tree is 15 . How tall is the tree?

May 5, 2015Geometry 9.5 Trigonometric Ratios w/o Calculator28 Summary Trig ratios are based on acute angles in right triangles. They are Sine, Cosine, Tangent. SOHCAHTOA Angle of elevation is from the ground up.