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3rd Quarter Mastery Test in Elective Math (Feb 23, 2021)

Total questions: 50

Worksheet time: 25mins

Name
Class
Date
1.

Based on the given information determine the number of unique triangles that may exist.

B= 70°, b=85, c=88

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

2.

Based on the given information determine the number of unique triangles that may exist.

A= 37°, a=8, b=14

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

3.

Based on the given information determine the number of unique triangles that may exist.

J = 98°, j = 29, p = 6

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

4.

Based on the given information determine the number of unique triangles that may exist.

A= 137°, a=8, b=8

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

5.

Based on the given information determine the number of unique triangles that may exist.

A= 70°, c= 90, B = 58°

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

6.

Based on the given information determine the number of unique triangles that may exist.

E= 38.7°, f = 203, e = 172

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

7.

Based on the given information determine the number of unique triangles that may exist.

V = 45°, v = 83, a = 79

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

8.

Based on the given information determine the number of unique triangles that may exist.

d = 8, D = 49°, B = 57°

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

9.

Based on the given information determine the number of unique triangles that may exist.

K = 123°, k = 18, j = 12

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

10.

Based on the given information determine the number of unique triangles that may exist.

V = 29°, v = 12, w = 15

a)

1 Triangle

b)

2 Triangles

c)

3 Triangles

d)

No Triangle

11.

Clint is building a wooden swing set for his children. Each supporting end of the swing set is to be an A-frame constructed with two 10 foot long 4-by-4s joined at a 45 degree angle. To prevent the swing set form tipping over, Clint wants to secure the base of each A-frame to concrete footings. How far apart should the footings for each A-frame be?

a)

5.461 feet

b)

6 feet

c)

9.743 feet

d)

7.65 feet

12.

A triangle with two sides that measure 6 m and 8 m with an included angle of 137°.

a)

17.8m²

b)

14.6m²

c)

16.4m²

d)

12.9m²

13.

A triangle with two sides that measure 5 cm and 8 cm with an included angle of 39°

a)

15.9cm²

b)

15.3cm²

c)

12.6cm²

d)

16.2cm²

14.

Which of the following formulas shows the Law of Cosines?

a)

c2 = a2 + b2 - 4ac + cosA

b)

c2 = a2 - b2 - 2abcosC

c)

c2 = a2 + b2 - 2abcosC

d)

(cos A)/a = (cos B)/b

15.

If three sides of a triangle are given, the Law of ____ is used to solve the triangle.

a)

Sines

b)

Cosines

c)

Tangent

d)

Cosecents

16.

Find angle Z

a)

20.15°

b)

51.06°

c)

57.71°

d)

71.23°

17.

Use Law of Cosines to find angle T

a)

64.7°

b)

62.2°

c)

59.5°

d)

53.1°

18.

Find QR

a)

34.7 km

b)

31.1 km

c)

13.74

d)

2.2 km

19.

Find the missing side.

a)

521.1 in.

b)

22.8 in.

c)

19.2 in.

d)

15.9 in.

20.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

21.

Find the area of ABC to the nearest tenth.

a)

62.3 units2

b)

77.0 units2

c)

100 units2

d)

124.6 units2

22.

Solve each triangle. A=110, C=30, c=3

a)

B=40, a=5.64, b= 3.86

b)

B= 40, a= 7.90, b= 3.41

c)

B= 45, a= 6.93, b= 2.76

d)

B=40, a= 6.21, b= 3.86

23.

Maruel must find the distance from Point A to Point B on opposite sides of a lake. He locates Point C that is 860 feet from point A and 175 feet from Point B. He measures the angle at Point C to be 78 degrees. Find the distance from point A to point B.

a)

707643.58

b)

877.62

c)

842.01

d)

841.22

24.

Given: B = 70°, a = 11, C = 40° Find: c

a)

70

b)

11

c)

8.5

d)

7.5

25.

Solve the Triangle

a=38, b= 31, c= 35

Find A, B and C

a)

A= 43°, B= 47°, C= 90°

b)

A= 50.1°, B= 70°, C= 59.9°

c)

A= 70°, B= 50.1°, C= 59.9°

d)

A= 60°, B= 70°, C= 50°

26.

Find the area of ΔABC

if a = 9cm, b = 11cm, c = 16cm

a)

89.5 sq cm

b)

52.1 sq cm

c)

47.6 sq cm

d)

15.2 sq cm

27.

In triangle ABC, a = 5, b = 6, c = 7. Which law would you need to use first?

a)

Law of Sines

b)

Law of Cosines

c)

Both trig laws

d)

Pythagorean Theorem

28.

Find Area of ABC

a)

223.6 units2

b)

52.7 units2

c)

73.1 units2

d)

3.3 units2

29.

Choose which law you need to solve the problem (DO NOT SOLVE):

a)

Law of Sines

b)

Law of Cosines

c)

Both

d)

Neither

30.

In triangle ABC, a = 5, b = 6, c = 7. Which law would you need to use first?

a)

Law of Sines

b)

Law of Cosines

c)

Both trig laws

d)

Pythagorean Theorem

31.
a)

sin²θ

b)

tanθ

c)

cosθ

d)

1- sin²θ

32.

a)

-1

b)

1

c)

csc θ

d)

sin θ

33.

a)

1/cos x

b)

cot x

c)

1

d)

-1

34.

sin2 θ =

a)

1 - cos2θ

b)

sec2θ - 1

c)

1 - sin2θ

d)

csc2θ - 1

35.

cot θ =

a)

cosθ/sinθ

b)

sinθ/cosθ

c)

tanθ

d)

1/cosθ

36.
a)

csc2 x

b)

cot2 x

c)

sec2 x

d)

tan2 x

37.

-(sin²x + cos²x)

a)

-2

b)

-1

c)

1

d)

2

38.

sec θ =

a)

1/cosθ

b)

1/tanθ

c)

1/sinθ

d)

1/cscθ

39.

Simplify the trig expression.

a)

1

b)

-1

c)

-tanx

d)

tanx

40.

Simplify: sin x cot x

a)

cos x

b)

tan x

c)

sin x

d)

sec x

41.

Simplify: sin x cot x

a)

cos x

b)

tan x

c)

sin x

d)

sec x

42.

Simplify: tanxcotx-cos2x

a)

tanx

b)

cotx

c)

sin2x

d)

cos2x

43.

Is this a pythagorean identity?

tan2x + 1 = secx

a)

Yes

b)

No

44.

The expression sinA(cscA-sinA) is equivalent to

a)

1

b)

cos2A

c)

-sin2A

d)

cosA

45.
a)

sinx

b)

tan²x

c)

cot²x

d)

cosx

46.

a)

-1

b)

1

c)

csc θ

d)

sin θ

47.

a)

csc²θ

b)

cscθ

c)

sec²θ

d)

1

48.

a)

csc²θ

b)

cot θ tan θ

c)

csc θ sec θ

d)

1/sinθ

49.

a)

sinθ

b)

cos²θ

c)

sin²θ

d)

1- sin²θ

50.

a)

csc x

b)

1 + sec x

c)

1/sec x

d)

sec x

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