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Trigonometry Laws
Trigonometry Laws
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Explore the formulas and applications of the Law of Cosines and the Law of Sines in trigonometry
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1
What is the Law of Cosines formula?
a² = b² + c² - 2bc sin(A)
a² = b² + c² + 2bc cos(A)
a² = b² - c² - 2bc cos(A)
a² = b² + c² - 2bc cos(A)
2
Given A=35∘, a=14, and b=20, determine angle B.
55.8
57.5
37
53
3
Find the largest angle in a triangle with sides 4, 5, and 7.
103
101.5
4
Given A=45∘, a=14, and b=18, determine B.
65.2
65.3
5
Find angle B if A=50∘, a=15, and b=20.
1.201
none
2.3
1.021
6
Which angle is opposite side 'c'?
Angle D
Angle B
Angle C
Angle A
7
What is the Law of Sines formula?
a/tan(A) = b/sin(B) = c/sin(C)
a/sin(A) = b/cos(B) = c/tan(C)
a/sin(A) = b/sin(B) = c/sin(C)
a/cos(A) = b/sin(B) = c/sin(C)
8
sinB>1 when solving a triangle?
False
True
9
What is the cosine rule for angles?
cos(A) = (a² + b² - c²) / 2bc
cos(A) = (b² - c² + a²) / 2bc
cos(A) = (b² + c² - a²) / 2bc
cos(A) = (c² + a² - b²) / 2bc
10
True or false: You can use both laws together.
False
True
11
Can the Law of Sines be used in a right triangle?
True
False
12
Calculate tan45∘
1
2
13
ind the angle θ if sinθ=0.6
36.87
33.87
14
In a right triangle, if the hypotenuse is 10 and one of the legs is 6, find the length of the other leg.
b=19
b=8
15
In triangle XYZ, side x = 15 units, side y = 20 units, and angle Z = 40 °. Find angle X.
26.4°
20.1°
28.8°
31.7°
16
Find sin90∘.
1
2
17
Find C if a=5, b=7, and c=8.
75.4
73.4
18
Given A=40∘, B=75∘, and a=12, find b.
19.03
18.03
19
What are the given conditions for the SSA ambiguous case?
Two sides and a non-included angle, where multiple solutions may exist.
Two angles and a side, where only one triangle exists.
20
In what type of triangle does the Law of Sines fail to provide a unique solution?
none
ASA
SSA (Side-Side-Angle)
AAS
21
In triangle ABC, you know side a=9, side b=12, and side c=14. What is angle C?
89.1°
77.9°
88.5°
82.3°
22
In triangle DEF, angle D=40°, angle E=60°, and side e=12 units. Find the length of the side d.
7.2
13.4
12.1
8.9
23
How do you find an angle using the Law of Sines?
a² + b² = c²
sin(A)/a = sin(B)/b
tan(A) = opposite/adjacent
c² = a² + b² - 2ab cos(C)
24
In triangle ABC, angle B=98°, side a=10 cm, and side b= 32 cm. Fide angle A.
16.7°
18.0°
21.2°
19.9°
25
. What is cos60?
0.3
0.5
26
Suppose you have a triangle with the following known values: Side a=7, Side b= 10, and Angle A=40°. Find Angle B.
50.2°
66.9°
68.8°
70.1°
27
What is the smallest angle in a right triangle with legs of 3 and 4?
47.3
42.7
36.9
33.6
28
What is the value of cos0∘
1.3
1
29
Find b when a=7, c=9, and B=60
7.9
8.4
30
A triangle has sides a=8, b=12, and angle A=45∘∘. Find angle B.
77
75
74.5
76
31
Find sin30∘
0.3
0.5
32
Use the Law of Sines when given:
AAS
SSA
None of the above
ASA
33
Given a triangle with angles A=40∘, B=60∘∘, and side a=10, find side b.
14.9
cos40∘=cos60∘b
sin40∘10=sin60∘b
sin50∘=sin60∘b
34
True or false: is trigonometry used in physics?
True
False
35
In which of these following situations can you use the Law of Cosines to start solving the triangle?
You know a side and two angles
You know two angle measurements and the side between them
You know two sides and the included angles
You know all three angle measurements
36
When is Law of Cosines used?
One side and two angles
Right triangle
Two sides and included angle
All sides known
37
Find the missing side if A = 120∘, b = 8, and c=10.
15.6
16.7
38
In a right triangle, if the hypotenuse is 13 and one leg is 5, find the length of the other leg.
b=12
b=13
39
true or false the Law of Sines be used for an obtuse triangle
False
True
40
What is the largest angle in a triangle with sides of 6,7, and 8?
75.5
73.2
78.2
70.1
41
What do you need for the Law of Sines?
Two sides and one angle
Three sides only
Two angles and one side
One angle and two sides
42
True of False. Can the Law of Cosines be used to verify if a triangle is obtuse?
True
False
43
If a triangle has sides a=6, b=8, c=10, what type of triangle is it?
Right
Acute
Obtuse
44
Can the Law of Sines be used in a right triangle?
False
True
45
Given A=30∘, a=12a , B=45∘, find b.
16.97
16.03
21.97
15.98
46
What is the cosine rule formula?
a = b sin(C)
c² = a² + b² - 2ab cos(C)
a² + b² = c²
sin² + cos² = 1
47
Find side ccc in a triangle where A=35∘, B=55∘, and a=10
18.42
17.42
48
In a right triangle, if the opposite side is 3 and the adjacent side is 4, find tanθ.
0.75
0.77
49
What is the value of tan30∘?
0.675
0.577
