Geometry 9.5 Trigonometric Ratios
Geometry 9.5 Trigonometric Ratios w/o Calculator Goals Find the sine, cosine, and tangent of an acute angle. Solve problems using trigonometric ratios. November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Terminology No one, uses the word trigonometry. It’s Trig November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator 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. November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator What you will learn… The basic terms and methods of solving right triangles. How to use a trig table. How to solve problems using trig. November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Trig Ratios Based on the sides of a right triangle. We will study only three: Sine Cosine Tangent November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Right Triangle Hypotenuse Leg From A, this leg is the Opposite side. A Leg From A, this leg is the Adjacent side. November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Right Triangle B From B, this leg is the Adjacent side. Hypotenuse Leg From A, this leg is the Opposite side. A Leg From A, this leg is the Adjacent side. From B, this leg is the Opposite side. November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Right Triangle Hypotenuse Opposite A Adjacent November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Trig Ratio Definition: Sine Hypotenuse Opposite A Adjacent Opposite Sine of A = Hypotenuse November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Trig Ratio Definition: Cosine Hypotenuse Opposite A Adjacent Adjacent Cosine of A = Hypotenuse November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Trig Ratio Definition: Tangent Hypotenuse Opposite A Adjacent Opposite Tangent of A = Adjacent November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Abbreviations Sine of A = Opposite Hypotenuse sin A Cosine of A = Adjacent Hypotenuse cos A Tangent of A = Opposite Adjacent tan A November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Memory Aid Sine is Opposite over Hypotenuse. Cosine is Adjacent over Hypotenuse. Tangent is Opposite over Adjacent. SOHCAHTOA November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Writing Ratios SOHCAHTOA ? ? 3 4 5 A B ? ? ? ? ? ? ? ? ? ? November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Trig Table On page 845. Has Sine, Cosine and Tangent for angles from 1 to 89. For fractional values, use the nearest whole number of degrees. November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Using Trig Tables To find the sin 78: Locate 78 on page 845 in the column headed Angle. The Sine is the next column over. Sin 78 = .9781 November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Find these values: SIN 15 COS 45 TAN 45 COS 80 SIN 10 TAN 5 COS 60 SIN 90 .2588 .7071 1 .1736 .0875 .5 November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator 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. November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Example 1 Find x. From the 28 angle, x is the ? Opposite side, and 15 is the Hypotenuse. What trig ratio is this? Sine (SOHCAHTOA) 28 x 15 November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Example 1 Find x. Write the equation and solve. 28 x 15 November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Example 2 Find y. Write the equation and solve. 56 31 y November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Example 3 Find a. Write the equation and solve. a 40 8 November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Algebra Reminder Solve: November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Example 4 Find a. Write the equation and solve. 17 40 a November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Example 5 Find x & y. x y 78 150 November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Angle of Elevation Angle of Elevation Horizontal November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Angle of Depression Horizontal Angle of Depression November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator Problem Standing 30 yards from a tree, the angle of elevation to the top of the tree is 15. How tall is the tree? 30 yd 15 h November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator
Geometry 9.5 Trigonometric Ratios w/o Calculator 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. November 15, 2018 Geometry 9.5 Trigonometric Ratios w/o Calculator