Download Algebra 3-1

Honors Algebra II
Review- Right Triangle Trig, Law of Sines, Cosines
Name ________________________________________________
Fill in the ratios for each trig function using the letters for opposite (O), adjacent(A) and hypotenuse(H)
Sin =
Cos =
Tan =
Csc =
Sec =
Cot =
Find each value. No decimals – reduce fractions.
1. sin D
2. sin E
3. cot E
4. tan D
D
5. cos D
6. csc D
7. sec D
8. cot D
6
9. cos E
10. tan E
11. sec E
12. csc E
3 5
F
E
3
Let  be an acute angle of a right triangle. Find the value of the other five trigonometric functions of .
13. sin 
2
4
14. tan  
1
6
Cos  = ________ Tan  = ________
Sin  = ________ Cos  = ________
Sec  = ________ Csc  = ________ Cot  = ________
Sec  = ________ Csc  = ________ Cot  = ________
Using the 30-60-90 and 45-45-90 rules, find each length or angle measure. Express all lengths in simplest radical form.
15. AB = _____ BC = ______
A
16. PM = _____ MN = ______
P
18. ST = _____ TV =
______
S
12
9
3
C
17. AC = _____ AB = ______
A
60 
45 
B
N
45 
C
M
T
B
45 
V
15
Fill in the missing sides of the special triangles and answer the following questions. Exact answers only
19.
Sin 30 : _______
Cos 30: _______
Tan 30 : _______
20.
Sin 60 : _______
Cos 60: _______
Tan 60: _______
21.
Sin 45 : _______
8. Use a calculator set to find each
value. Round to the nearest 100th.
Sin 30 ____ Cos 30______ Tan 30
_____
Cos 45: _______
Sin 60 ____ Cos 60______ Tan 60
_____
Tan 45: _______
Sin 45 ____ Cos 45______ Tan 45
_____
How do the answers to the calculator questions
compare to the exact answers in 5-7?
Use a calculator to find each value. Round answers to the nearest hundredth.
23. cos 20
24. sin 10
25. tan 57
*26. csc 15 Just think, what does csc =
??
Use your calculator to find the measure of the angle that has each sin, cos, etc. Round decimal answers to the nearest hundredth.
27. sin x = 0.4899
28. cos x = 0.8258
29. cos x = 0.5240
30. tan x = 0.2074
Use SOH CAH TOA to solve for the following parts of the right triangles
31. c = 21, a = 15, find b
32. a = 32, b = 15, find A
33. A = 32, c = 8, find b
A
A
b
C
c
a
A
b
B
C
c
a
A
b
B
C
34. a = 5, b = 10, find B
c
a
b
B
C
c
a
B
Use SOH CAH TOA to solve each story problem
35. Katlyn leans a 16 foot ladder against the wall. If
the ladder makes an angle of 70° with the ground, how
far up the wall does the ladder reach?
36. A security light is being installed outside of
Lakeside Mall. The light needs to light up a
parking lot that is 150 feet long and it makes an
angle of 25º with the ground. How far up the
wall should the light be installed?
37. An airplane begins its descent which
makes a 10º angle with the ground. It has to
travel 500,000 ft in the air to reach the airport.
What is the ground distance between the
airport and the point on the ground directly
below the plane?
38. Tom leans a 20-ft ladder against a wall. The base
of the ladder
is 4 feet from the wall. What angle
 does the ladder make with the ground?
39. Samantha is standing 350 feet away from a
skyscraper that is 750 feet tall. What is the angle
of elevation to the top of the building?
40. Mike is in a boat that is floating 175 feet
from the base of a 200-ft cliff. What is his
angle of elevation to the top of the cliff?
State the Law of Sines:
State the Law of Cosines:
Use the Law of Sines and/or the Law of Cosines to solve each triangle. Round all decimals to the nearest 100th.
41.
42.
A =_________
B =_________ b =__________
A =_________
44.
C =_________ b =__________
a =_________ c =__________
A =_________
B =_________ C =__________
43.
A =_________
Use the Law of Sines and/or the Law of Cosines to solve each story problem. Round all decimals to the nearest 100th.
45. A pole is standing at an 83 angle and casts a shadow
that is 47 ft. long. If the angle of elevation of the sun is
51, how tall is the pole?
46. An isosceles triangle has a base of 22 cm and a
vertex angle of 36. Find the perimeter of the triangle.
47. A triangular lot has sides 120 ft, 150 ft
and 100 ft long. Find the angles of the lot.
48. Two forest rangers, 12 miles from each other on a
straight service road, both sight an illegal bonfire away
from the road. Using their radios to communicate with
each other, they determine that the fire is between them.
The first ranger’s line of sight to the fire makes an angle of
38 with the road, and the second ranger’s line of sight to
the fire makes a 63 angle with the road. How far is the fire
from each ranger?
fire
Ranger #1
49. A surveyor is measuring the width of a pond. The
transit is setup at a point C and forms an angle of 37
from point A to point B. The distance from point C to
point A is 54 feet and the distance from point C to point
B is 72 feet. How wide is the point from point A to
point B?
One leg of a right triangle is 4 times as
long as the other leg. Find the measure of
the two acute angles. (hint: you may make up
50.
numbers to use for the sides of the legs, as long as
one is 4 times the other…)
Ranger #2
Area of Triangles – Use Area =
51. b = 8, c = 15, mA = 30
1
bcsin A or an equivalent equation to find each area
2
52. b = 1, c = 1, mA = 10
53. Yet another formula for area of a triangle is Hero or Heron’s formula given as: Area 
s s  a s  b s  c  where
1
s  a  b  c  and a, b, and c are the sides. Use this formula to find the area of this triangle.
2