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

2. 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

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

4. 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

5. 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

6. 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

7. 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

8. 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

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

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

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

12. 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

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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

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

21. 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

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

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

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

25. 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

26. 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