Geometry 9.5 Tangent Ratio How can you find a missing leg length on a right triangle when you only know one length?

Geometry 9.4 Tangent Ratio Goals Find the tangent of an acute angle. Solve problems using trigonometric ratios. April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Terminology No one, uses the word trigonometry. It’s Trig April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio 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. April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio 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. April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Trig Ratios Based on the sides of a right triangle. We will study only three: Sine Cosine Tangent This one today April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Right Triangle Hypotenuse Leg From A, this leg is the Opposite side. A Leg From A, this leg is the Adjacent side. April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio 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. April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Right Triangle Hypotenuse Opposite A Adjacent April 12, 2018 Geometry 9.4 Tangent Ratio

Trig Ratio Definition: Tangent Hypotenuse Opposite A Adjacent Opposite Tangent of A = Adjacent April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Abbreviations Tangent of A = Opposite Adjacent tan A April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Memory Aid Sine is Opposite over Hypotenuse. Cosine is Adjacent over Hypotenuse. Tangent is Opposite over Adjacent. SOHCAHTOA April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Writing Ratios ? ? 3 4 5 A B ? ? ? ? ? ? ? ? ? ? April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Trig Table Handout Has Sine, Cosine and Tangent for angles from 1 to 89. For fractional values, use the nearest whole number of degrees. April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Using Trig Tables To find the sin 78: Locate 78 in the column headed Angle. The Sine is the next column over. Sin 78  = .9781 April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Find these values: You can use the table or calculator. Today we focus on Tan. Sin and Cos will be the next lesson. SIN 15 COS 45 TAN 45 COS 80 SIN 10 TAN 5 COS 60 SIN 90 .2588 .7071 1 .1736 .0875 .5 April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio 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. Solve. April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio 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 April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Example 1 Find a. Write the equation and solve. a 40 8 April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Algebra Reminder Solve: April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Example 2 Find a. Write the equation and solve. 17 40 a April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Example 5 Find x x 78 150 April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Angle of Elevation Angle of Elevation Horizontal April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Angle of Depression Horizontal Angle of Depression April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio 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 April 12, 2018 Geometry 9.4 Tangent Ratio

Geometry 9.4 Tangent Ratio Summary Trig ratios are based on acute angles in right triangles. They are Sine, Cosine, Tangent. Angle of elevation is from the ground up. April 12, 2018 Geometry 9.4 Tangent Ratio