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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