1. Geometry
9.5 Trigonometric Ratios

2. Geometry 9.5 Trigonometric Ratios w/o Calculator
Goals
I can find the sine, cosine, and tangent of an acute angle.
I can solve problems using trigonometric ratios.
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

3. Geometry 9.5 Trigonometric Ratios w/o Calculator
Terminology
No one, uses the word trigonometry.
It’s
Trig
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

4. 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.
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

5. Geometry 9.5 Trigonometric Ratios w/o Calculator
What you will learn…
The basic terms and methods of solving right triangles.
How to solve problems using trig.
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

6. 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
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

7. 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.
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

8. 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.
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

9. Geometry 9.5 Trigonometric Ratios w/o Calculator
Right Triangle
Hypotenuse
Opposite A
Adjacent
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

10. Trig Ratio Definition: Sine
Hypotenuse
Opposite A
Adjacent
Opposite
Sine of A =
Hypotenuse
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

11. Trig Ratio Definition: Cosine
Hypotenuse
Opposite A
Adjacent
Adjacent
Cosine of A =
Hypotenuse
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

12. Trig Ratio Definition: Tangent
Hypotenuse
Opposite A
Adjacent
Opposite
Tangent of A =
Adjacent
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

13. 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
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

14. 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
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

15. Writing Ratios SOHCAHTOA? ? 3 4 5 A B ? ? ? ? ? ? ? ? ? ?
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

16. Geometry 9.5 Trigonometric Ratios w/o Calculator
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 90
.2588
.7071 1
.1736
.0875 .5
The sine of one angle
Is the same as the
cosine of its complement.
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

17. 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.
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

18. 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
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

19. Geometry 9.5 Trigonometric Ratios w/o Calculator
Example 1 Find x.
Write the equation and solve.
28 x 15
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

20. Geometry 9.5 Trigonometric Ratios w/o Calculator
Example 2 Find y.
Write the equation and solve. 56
31 y
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

21. Geometry 9.5 Trigonometric Ratios w/o Calculator
Example 3 Find a.
Write the equation and solve. a
40 8
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

22. Geometry 9.5 Trigonometric Ratios w/o Calculator
Algebra Reminder
Solve:
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

23. Geometry 9.5 Trigonometric Ratios w/o Calculator
Example 4 Find a.
Write the equation and solve. 17
40 a
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

24. Geometry 9.5 Trigonometric Ratios w/o Calculator
Example 5 Find x & y. x y
78
150
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

25. Geometry 9.5 Trigonometric Ratios w/o Calculator
Angle of Elevation
Angle of Elevation
Horizontal
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

26. Geometry 9.5 Trigonometric Ratios w/o Calculator
Angle of Depression
Horizontal
Angle of Depression
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

27. 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
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator

28. 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.
January 30, 2018
Geometry 9.5 Trigonometric Ratios w/o Calculator