Download Special Right Triangles

Algebra 2
Unit 8
13.1: Right Triangle Trigonometry
Name: _______________________________________
Block: __________
Solve for missing ANGLE
Solving for missing SIDES
1.) Given two angles, subtract from
________ to find the 3rd
1) Pythagorean Theorem: When given _____ _____________.
2) Special Right Triangle: _______________ & _______________
3) Trigonometry: _____________________
***Last resort because a results in a decimal which is __________
__________________ than a radical!
2) Trigonometry: The missing
angle is usually referred to as
______________________.
*Use the _________________ trig
functions:
Pythagorean Theorem:
 Only works with
triangles
**The _____________________ is
across from the right angle and is
always the ______________ side.**
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
3.
1016
12
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:
45
45
Case 2: 30-60-90: _______________________________________________________
Example:
30
30
60
60
Practice: Use special right triangles to determine the length of the missing sides. Leave your answers exact –
NO decimals!!!
4.
5.
**6.
60˚
30˚
7
45˚
6
7.
8.
10
45˚
**9.
30˚
12
8
45˚
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:
Remember
Soh Cah Toa
sin  =
θ
cos  =
tan  =
θ
Write 3 basic trigonometric ratios for the following triangle.
A
sin  =
3
cos  =
5
θ
sin A =
sin B =
cos A =
cos B =
tan A =
tan B =
6
tan  =
B
4
C
3 3
Use a calculator to complete. REMEMBER TO BE IN ________________ MODE!!!
10)
cos 22  _____
11)
sin 79  ____
13)
sin 54° =
16)
sin 70° =
12)
tan 43  _____
x
9
14)
cos 20° =
x
52
15)
tan 35° =
x
25
3
x
17)
cos 54° =
14
x
18)
tan 54° =
82
x
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 = _____
x
52
14
27
10
x
72
10
y
Work:
Using Inverse Trig to Solve for MISSING ANGLES

_____________

_____________

_____________
All three inverse trig. functions are
found on your calculator:
Press 2nd
 and then select the trig.
function you want to use!
Solve for x.
22.) sin x° =
2
7
23.) cos x° =
10
17
24.) tan x° =
2
5
Examples: Solve for the missing angle using the two sides that are given:
25.)
26.)
27.)
10
52
3
5
17
12.5
x