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Lesson 32. Right Triangle Trigonometry
Advanced Algebra B
Reference: McDougal Littell § 13.1 Use Trigonometry with Right Angles. Pages 852-855 See Examples 1-6
Right Triangle Trigonometry
Let  be an acute angle in a right triangle. Then the following ratios are always the same…
opposite
hypoteneuse
adjacent
cos  
hypoteneuse
opposite
tan  
adjacent
hypoteneuse
opposite
hypoteneuse
sec  
adjacent
adjacent
cot  
opposite
sin  
hypotenuse
csc  
opposite
.

adjacent
csc  
1
sin 
sec  
1
cos 
cot  
1
tan 
1. SOH-CAH-TOA is a useful mneumonic device to remember trig ratios
Evaluate.
7 cm


24 cm
sin() =
sin() =
cos() =
cos() =
tan() =
tan() =
2. Special Triangles: 30-60-90 Triangle
Evaluate.
sin(30) =
1
sin(60) =
cos(30) =
cos(60) =
tan(30) =
tan(60) =
3. Special Triangles: 45-45-90 Triangle
Evaluate.
sin(45) =
csc(45) =
60
30
3
2
45
1
2
2
45
1
2
cos(45) =
sec(45) =
tan(45) =
cot(45) =
2
2
Special Values of the Trigonometric Functions to Remember
degrees
0
30
45
60
90
sin(θ)
=
cos(θ)cos(45)
tan(θ)
tan(45) =
1
60
1
2
30
3
2
45
1
45
2
2
2
2
4. SOH-CAH-TOA
Given sin  = 3/5, find each of the following.
5. SOH-CAH-TOA
Given cos  = 12/13, find the following.
(a) csc  =
(a)
cot  =
(b)
sin  =
(c) sec  =
(c)
tan  =
(d) tan  =
(d)
sec  =
(e) cot  =
(e)
csc  =
(b) cos  =

6. Application
A moving van has a ramp that makes a 40° angle with the
road. If the distance from the back of the truck to the
road is 3.25 ft, find the measure the lengths of the
unknown sides in the ramp and the unknown angle.

B
l1
A
h = 3.25 ft
40
C
l2
Additional Problems
1. p856 #4
2. p856 #5
3. p856 #6
4. p856 #10
5. p856 #11
6. p856 #12
7. p856 #18
8. p856 #19
9. p856 #22
10. p856 #24
11. p856 #30
12. p856 #32
Application Problem
13. A handicap ramp rises at an angle of 30 over a distance of
12 feet, as shown in the diagram at the right.
(a) How long is the ramp? Express your answer in
simplest radical form, then approximate your
answer in feet and inches, to the nearest inch.
ramp
30
12 feet
(b) How high does the ramp rise? Express your answer
in simplest radical form, then approximate your
answer in feet and inches, to the nearest inch.
Review
Tell whether each of the following sequences is arithmetic, geometric or neither. Find an explicitly or
recursively.
14. {5, 9, 13, 17, …}
15. {3, 6, 12, 24, …}
16. 40,10, 52 , 58 ,...
17. {4, 7, 12, 19, …}
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