Algebra 2 Trig 1



Algebra 2 Name: _______________________________________

Unit 8 Block: __________

13.1: Right Triangle Trigonometry

Pythagorean Theorem:

❖ Only works with triangles

Practice: Find the measure of the third/missing side of the following triangles. Leave answers as radicals if necessary. NO DECIMALS!

1. 2. 3.

4

GIVEN: One Side of a Right triangle and a Special Case Angle: 45˚, 30˚, or 60˚

Special Right Triangles: There are two special right triangles.

Case 1: 45(-45(-90(: ________________________________________________________

Example:

Case 2: 30(-60(-90(: _______________________________________________________

Example:

Practice: Use special right triangles to determine the length of the missing sides. Leave your answers exact – NO decimals!!!

4. 5. **6.

7. 8. **9.

Trig! Remember, when finding a side length, try Pthag. Thm. or a Special Right BEFORE trig!

GIVEN:

One Side of a Right triangle and a Non-Special Angle: (NOT 45˚, 30˚, or 60˚)

***Two Sides of a Right triangle and you need to find an angle

The ratios formed by the

sides have names/labels:

Write 3 basic trigonometric ratios for the following triangle.

sin ( = sin A = sin B =

cos ( =

cos A = cos B =

tan ( =

tan A = tan B =

Use a calculator to complete. REMEMBER TO BE IN ________________ MODE!!!

10) cos 22( ( _____ 11) sin 79( ( ____ 12) tan 43( ( _____

13) sin 54° = [pic] 14) cos 20° = [pic] 15) tan 35° = [pic]

16) sin 70° = [pic] 17) cos 54° = [pic] 18) tan 54° = [pic]

Using Trig to Solve for missing sides

Find the value of x & y to the nearest tenth. Show the trig ratio.

19. x = _________ 20. x = _________ 21. x = _____ y = _____

Work:

Using Inverse Trig to Solve for MISSING ANGLES

• _____________

• _____________

• _____________

Solve for x.

22.) sin x° = [pic] 23.) cos x° = [pic] 24.) tan x° = [pic]

Examples: Solve for the missing angle using the two sides that are given:

25.) 26.) 27.)

-----------------------

Solve for missing ANGLE

1.) Given two angles, subtract from ________ to find the 3rd

2) Trigonometry: The missing angle is usually referred to as

______________________.

*Use the _________________ trig functions:

Solving for missing SIDES

1) Pythagorean Theorem: When given _____ _____________.

2) Special Right Triangle: _______________ & _______________

3) Trigonometry: _____________________

***Last resort because a results in a decimal which is __________

__________________ than a radical!

**The _____________________ is across from the right angle and is always the ______________ side.**

16

12

3

10

45(

45(

30(

60(

30(

60(

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7

45˚

30˚

6

[pic]

45˚

10

8

45˚

30˚

12

Remember

Soh Cah Toa

sin ( = cos ( = tan ( =

θ

θ

6

A

B

C

[pic]

4

5

3

θ

x

27

52(

14

x

10(

72(

10

y

x

All three inverse trig. functions are found on your calculator:

Press 2nd

( and then select the trig.

function you want to use!

12.5

52

[pic]

17

3

[pic]

5

10

[pic]

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