1. 13.1 – Use Trig with Right Triangles

2. Hypotenuse:
Opposite side:
Adjacent side:
Side opposite right angle
Hypotenuse
Opposite 
Side opposite reference angle
Adjacent
Side next to reference angle, not hypotenuse

3. opp hyp adj hyp opp adj sin  = cos  = tan  = hyp opp hyp adj adj
Hypotenuse
Opposite
hyp
opp
hyp
adj
adj
opp
csc  =
sec  =
cot  = 
Adjacent
1 .
sin 
1 .
cos 
1 .
tan 
csc  =
sec  =
cot  =
csc =
cosecant
SOH – CAH – TOA
sec =
secant
cot =
cotangent

4. 1. Evaluate the six trigonometric functions of the angle .
c2 = a2 + b2 H O
152 = a2 + 92
225 = a2 + 81
144 = a2
12 = a 12 A 9 15 12 15 9 12
sin  =
cos  =
tan  = 15 9 15 12 12 9
csc  =
sec  =
cot  =

5. 2. Let  be an acute angle of a right triangle
2. Let  be an acute angle of a right triangle. Find the value of the other five trigonometric functions of .
c2 = a2 + b2 H O
52 = a2 + 42 5 4
25 = a2 + 16 
9 = a2 3 A
3 = a 4 5 3 5 4 3
sin  =
cos  =
tan  = 5 4 5 3 3 4
csc  =
sec  =
cot  =

6. H O A c2 = a2 + b2 2 1 adj opp cot  = c2 = 1 + 3 c2 = 4 c = 2 4 5 3 5
2. Let  be an acute angle of a right triangle. Find the value of the other five trigonometric functions of .
c2 = a2 + b2 H O 2 1
adj
opp
cot  =
c2 = 1 + 3 
c2 = 4 A
c = 2 4 5 3 5 4 3
sin  =
cos  =
tan  = 5 4 5 3 3 4
csc  =
sec  =
cot  =

7. H O A c d c 7 d 7 sin 42° = cos 42° = 1 1 7  sin 42° = c
3. Find the measure of the missing sides. Round to the nearest hundredth. c d H O c 7 d 7
sin 42° =
cos 42° = 1 1
7  sin 42° = c
7  cos 42° = d A
4.68 = c
5.20 = d
SOH – CAH – TOA

8. H A O a b 14 a 14 b tan 57° = sin 57° = 1 1 a  tan 57° = 14
3. Find the measure of the missing sides. Round to the nearest hundredth. a b H A 14 a 14 b
tan 57° =
sin 57° = 1 1 O
a  tan 57° = 14
b  sin 57° = 14
a = 9.09
16.69 = b
SOH – CAH – TOA

9. H A O A = 40°, c = 8 A B C a b c 40° SOH – CAH – TOA 8 50° 90° 5.14 a
4. Solve ABC, using the diagram and the given measurements.
A = 40°, c = 8 A B C a b c
40°
SOH – CAH – TOA H 8
50° A
40°
90° O
5.14 a b
6.13 a 8 b 8
sin 40° =
cos 40° = 8 1 1
8  sin 40° = a
8  cos 40° = b
a = 5.14
6.13 = b

10. Remember special triangles?
45°
90°
30°
60°
90° 1 1 1 2
45°
60° 1 2 1
45°
30° 1

11. 5. Find the exact values of the variables.13 1
y = 1

12. 5. Find the exact values of the variables.1
x =
60°
y = 14 2

13. 5. Find the exact values of the variables.3 1
y = 2

14. 5. Find the exact values of the variables.1 2
y =