Algebra 2
Practice – Ch. 13
To find a missing side use:
To find a missing angle use:
To find a coterminal angle:
To find a reference angle:
To find coordinates of a point:
To find arc length:
1.)
*The angle MUST BE IN _________!
Solve the triangle. Give angle measures to the nearest degree and side lengths to
the nearest tenth.
N
a.)
mP = ________
5
13
M
b.)
mN = _______
c.)
PM = ________
2)
3.)
P (4, -7) is a point on the terminal side of  in standard position . Find the exact
values for the indicated functions.
sin  = _________
csc  = __________
cos  =
_____
sec  = __________
tan  = _________
cot  = __________
Convert from radians to degrees or from degrees to radians.
a.)
4.)
P
-120o
b.)
63o
c.)
3
8
d.)
10
3
A driver uses a ramp when unloading supplies from his delivery truck. The ramp is 10 ft long
and the bed of the truck is 4 feet off the ground. To the nearest degree, what angle does the
ramp make with the ground?
5.)
Solve the triangle. Give angle measures to the nearest degree and side lengths to
the nearest tenth.
E
F
a.)
53
5.4
mE =
G
b.)
EF =
c.)
GF =
6.
Find the coterminal angle of 100° so that the angle is between -360° and 360°.
7.
Find the reference angle for 240°.
8.
What are the coordinates on the unit circle of the point (x, y) for 210°?
9.
Find the length of an arc whose angle is 100° and diameter is 16. Round to the nearest tenth.
10.
A biologist’s eye is 5.5 ft above the ground. She measures the angle of elevation to an eagle’s
nest on a cliff to be 66o when she stands 50 ft from the cliff’s base. To the nearest foot, what
is the height of the eagle’s nest?
For 225°?
Answers
2]
7
4 65 7 65
;
;  ;
65
65
4
4]
24o
6]
-260o
60o
8]
  3 1 
, ;


 2 2
13.96
10]
129 ft
1]
P = 22.62o
N = 67.38o
3]
7
2
;
; 67.5o ; -600o
20
3
5]
E = 37o
7]
9]
EF = 6.76
PN = 12
GF = 4.07
65
;
4
 2  2
,


2 
 2
4
65
; 
7
7
Chapter 13 Review continued:
Law of Sines (AAS & ASA & SSA – ambiguous)
Law of Cosines (SAS & SSS)
Area of Triangle (given SAS)
Heron’s Formula for Area
1.)
3.)
Given: m C  115  , m A  35 
and b = 25. Find the length of c.
Round to the nearest hundredth.
Given: m C  86  , b = 12 and a = 8.
Find the area of the triangle.
Round to the nearest tenth.
Answers
1]
c = 45.32
2]
A = 28.9o
3]
4]
325 ft2
area = 47.9
2.)
Given: a = 1.0, b = 2.0, c = 1.5.
Find the missing angles.
Round to nearest tenth.
4.)
Given: a = 22ft, b = 30ft and c = 34 ft.
Find the area of the triangle.
Round to the nearest square foot.
B = 104.5o
C = 46.6o
Chapter 13
1. Solve the triangle. Give angle measures to the nearest degree and side lengths to the nearest tenth.
J
a. JK = ________
b. mJ = ________
8
c. mK = ________
L
12
K
2. Solve the triangle. Give angle measures to the nearest degree and side lengths to the nearest tenth.
a. mM = ________
N
26˚
b. MN = ________
c. NO = _________
O
9.7
M
For each angle below find all coterminal angles such that -360˚ < θ < 360˚. Then find the reference angle for
the given angle.
3. 114˚
4. 512˚
5. -53˚
Given the point on the terminal side of  in standard position, find the exact value of the trig functions listed.
6. P (-5, -12) find sin θ and cos θ
7. P (7, -2) find csc  and cot 
Convert each degree measure to a radian measure. Give each exact answers.
8. 20˚
9. 1080˚
Convert each radian measure to a degree measure. Round answers to the nearest tenth of a degree, if necessary.
2
3
10.
radians
11. 
radians
3
4
Evaluate each expression.
5
12. cos
6
 3
C os1 
 2  = _______ degrees


13. tan 
3
4
14. csc
T an1 1 = ________radians

6
1
Sin 1   = _______ degrees
2
A circle has a diameter of 8 meters. For each central angle measure below, find the length in meters of the arc
intercepted by the angle.

15.
radians
16. 2.5 radians
12
Solve the triangles using the given information.
17. A = 65˚, C = 20˚, b = 9
18. B = 50˚, C = 32˚, a = 35
19. a = 13, b = 15, c = 9
20. b = 42, c = 30, A = 56˚
State the number of triangles determined by the given information. If 1 or 2 triangles are formed, solve the
triangle(s). Round the angle measures and side lengths to the nearest tenth.
21. A = 117˚, b = 40, a = 28
22. B = 39˚, a = 4, b = 3