9 5 Tangent Ratio Geometry How can you

9. 5 Tangent Ratio Geometry How can you find a missing length on a right triangle when you only know one length?

Goals n n Find the tangent of an acute angle. Solve problems using trigonometric ratios. 09 January 2022 Geometry 9. 4 Tangent Ratio 2

Terminology n n No one, uses the word trigonometry. It’s 09 January 2022 Geometry 9. 4 Tangent Ratio 3

What is trig? n n 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. 09 January 2022 Geometry 9. 4 Tangent Ratio 4

What you will learn… n n n The basic terms and methods of solving right triangles. How to use a trig table. How to solve problems using trig. 09 January 2022 Geometry 9. 4 Tangent Ratio 5

Trig Ratios n n n Based on the sides of a right triangle. We will study only three: Sine Cosine Tangent This one today 09 January 2022 Geometry 9. 4 Tangent Ratio 6

Right Triangle e t o p Hy A e s u n Leg From A, this leg is the Opposite side. Leg From A, this leg is the Adjacent side. 09 January 2022 Geometry 9. 4 Tangent Ratio 7

Right Triangle B e t o p Hy A e s u n From B, this leg is the Adjacent side. Leg From A, this leg is the Opposite side. Leg From A, this leg is the Adjacent side. From B, this leg is the Opposite side. 09 January 2022 Geometry 9. 4 Tangent Ratio 8

Right Triangle e t o p Hy A 09 January 2022 e s u n Opposite Adjacent Geometry 9. 4 Tangent Ratio 9

Trig Ratio Definition: Tangent e t o p Hy A e s u n Opposite Adjacent Opposite Tangent of A = Adjacent 09 January 2022 Geometry 9. 4 Tangent Ratio 10

Abbreviations Opposite Tangenttan of A A = Adjacent 09 January 2022 Geometry 9. 4 Tangent Ratio 11

Memory Aid n n n Sine is Opposite over Hypotenuse. Cosine is Adjacent over Hypotenuse. Tangent is Opposite over Adjacent. SOHCAHTOA 09 January 2022 Geometry 9. 4 Tangent Ratio 12

Writing Ratios ? ? ? 09 January 2022 ? B 5 3 4 Geometry 9. 4 Tangent Ratio A ? ? ? 13

Trig Table n n n Handout Has Sine, Cosine and Tangent for angles from 1 to 89. For fractional values, use the nearest whole number of degrees. 09 January 2022 Geometry 9. 4 Tangent Ratio 14

Using Trig Tables n n To find the sin 78 : Locate 78 in the column headed Angle. The Sine is the next column over. Sin 78 =. 9781 09 January 2022 Geometry 9. 4 Tangent Ratio 15

Find these values: n n n n 09 January 2022 SIN 15 COS 45 TAN 45 COS 80 SIN 10 TAN 5 COS 60 SIN 90 n n n n . 2588. 7071 1. 1736. 0875. 5 1 Geometry 9. 4 Tangent Ratio You can use the table or calculator. Today we focus on Tan. Sin and Cos will be the next lesson. 16

Solving Triangles n n n 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. 09 January 2022 Geometry 9. 4 Tangent Ratio 17

Example 1 Find x. From the 28 angle, x is the ? Opposite side, and 15 is the x Hypotenuse. 15 28 What trig ratio is this? Sine (SOHCAHTOA) 09 January 2022 Geometry 9. 4 Tangent Ratio 18

Example 1 Find a. Write the equation and solve. a 40 8 09 January 2022 Geometry 9. 4 Tangent Ratio 19

Algebra Reminder n Solve: 09 January 2022 Geometry 9. 4 Tangent Ratio 20

Example 2 Find a. Write the equation and solve. 17 40 a 09 January 2022 Geometry 9. 4 Tangent Ratio 21

Example 5 Find x x 78 150 09 January 2022 Geometry 9. 4 Tangent Ratio 22

Angle of Elevation Horizontal 09 January 2022 Geometry 9. 4 Tangent Ratio 23

Angle of Depression Horizontal Angle of Depression 09 January 2022 Geometry 9. 4 Tangent Ratio 24

Problem Standing 30 yards from a tree, the angle of elevation to the top of the tree is 15. How tall is the tree? h 15 30 yd 09 January 2022 Geometry 9. 4 Tangent Ratio 25

Summary n n n Trig ratios are based on acute angles in right triangles. They are Sine, Cosine, Tangent. Angle of elevation is from the ground up. 09 January 2022 Geometry 9. 4 Tangent Ratio 26