Free Printable Sides of Right Triangles

1.

Use the 45-45-90 theorem to solve for the hypotenuse.

a)

16

b)

8

c)

8√2

d)

√16

2.

Find x.

a)

10

b)

10√3

c)

10√2

d)

20

3.

Find x.

a)

22

b)

11√3

c)

11√2

d)

11

4.

Find a.

a)

12

b)

24

c)

24√3

d)

16

5.

Find a.

a)

2√3

b)

2

c)

12

d)

6

6.

Find x.

a)

9

b)

3√3

c)

6

d)

6√3

7.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

8.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

9.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Isosceles

d)

Obtuse

10.

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

11.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

12.

Find the length of m.

a)

4

b)

6

c)

12

d)

2√3

13.

Determine the value of x.

a)

x = 10√2

b)

x = 10

c)

x = 5√3

d)

x = 5√6

14.

Determine the value of x.

a)

x = 8√2

b)

x = 16√2

c)

x = 16

d)

x = 8√6

15.

Determine the value of c.

a)

c = 6√3

b)

c = 12√3

c)

c = 18

d)

c = 18√2

16.

Determine the length of x.

a)

x = 3/2

b)

x = 3

c)

x = 3√3

d)

x = 6

17.

Determine the area of the entire diagram shown. The area of a triangle is A = ½bh

a)

10√2

b)

20√2

c)

200

d)

400

18.

Find x.

a)

10

b)

10√3

c)

10√2

d)

20

19.

Find x.

a)

22

b)

11√3

c)

11√2

d)

11

20.

Find a.

a)

12

b)

24

c)

24√3

d)

16

21.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

22.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

23.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

24.

What is the length of x in this picture?

a)

45

b)

5√2

c)

90

d)

5

25.

What is the length of y in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

26.

Which is the length of v in this 30-60-90 triangle?

a)

$4\sqrt{3}$

b)

4

c)

8

d)

$4\sqrt{2}$

27.

What is the length of the short leg of this 30-60-90 triangle?

a)

6

b)

$\frac{6}{\sqrt{3}}$

c)

3

d)

$\frac{6}{\sqrt{2}}$

28.

What is x in this 30-60-90 triangle?

a)

x = 6

b)

x = 3√2

c)

x = 3√3

d)

x = 3√3

29.

What is y in this 30-60-90 triangle?

a)

$y=6$

b)

$y=3\sqrt{2}$

c)

$y=3\sqrt{3}$

d)

$y=\frac{3}{\sqrt{3}}$

30.

What is a in this 30-60-90 triangle?

a)

a = 7√3

b)

a = 7√2

c)

a = 14

d)

a = 14√3

31.

What is the measure of side b?

a)

5

b)

10√2

c)

$\frac{10}{\sqrt{2}}$

d)

10√3

32.

What is the length of y in this triangle?

a)

14

b)

$7\sqrt{3}$

c)

3.5

d)

$\frac{7}{\sqrt{3}}$

33.

What is the length of x in this triangle?

a)

14

b)

$7\sqrt{3}$

c)

3.5

d)

$\frac{14}{\sqrt{3}}$

34.

In this isosceles triangle, what is the length of x?

a)

8√2

b)

$\frac{8}{\sqrt{2}}$

c)

16

d)

8

35.

In this 30-60-90 triangle, what is the length of the hypotenuse?

a)

4√2

b)

4√3

c)

4

d)

8

36.

In this 30-60-90 triangle, what is the length of the long leg?

a)

6√2

b)

3√3

c)

12

d)

6√3

37.

What is b in this 30-60-90 triangle?

a)

b=3.5√3

b)

b = 3.5

c)

b = 7

d)

b = 7√3

38.

Find x.

a)

10

b)

10√3

c)

10√2

d)

20

39.

Find x.

a)

22

b)

11√3

c)

11√2

d)

11

40.

Find a.

a)

12

b)

24

c)

24√3

d)

16

41.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

42.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

43.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

44.

What is the length of x in this picture?

a)

45

b)

5√2

c)

90

d)

5

45.

What is the length of y in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

46.

Which is the length of v in this 30-60-90 triangle?

a)

$4\sqrt{3}$

b)

4

c)

8

d)

$4\sqrt{2}$

47.

What is the length of the short leg of this 30-60-90 triangle?

a)

6

b)

$\frac{6}{\sqrt{3}}$

c)

3

d)

$\frac{6}{\sqrt{2}}$

48.

What is x in this 30-60-90 triangle?

a)

x = 6

b)

x = 3√2

c)

x = 3√3

d)

x = 3√3

49.

What is y in this 30-60-90 triangle?

a)

$y=6$

b)

$y=3\sqrt{2}$

c)

$y=3\sqrt{3}$

d)

$y=\frac{3}{\sqrt{3}}$

50.

What is a in this 30-60-90 triangle?

a)

a = 7√3

b)

a = 7√2

c)

a = 14

d)

a = 14√3

51.

What is the measure of side b?

a)

5

b)

10√2

c)

$\frac{10}{\sqrt{2}}$

d)

10√3

52.

What is the length of y in this triangle?

a)

14

b)

$7\sqrt{3}$

c)

3.5

d)

$\frac{7}{\sqrt{3}}$

53.

What is the length of x in this triangle?

a)

14

b)

$7\sqrt{3}$

c)

3.5

d)

$\frac{14}{\sqrt{3}}$

54.

In this isosceles triangle, what is the length of x?

a)

8√2

b)

$\frac{8}{\sqrt{2}}$

c)

16

d)

8

55.

In this 30-60-90 triangle, what is the length of the hypotenuse?

a)

4√2

b)

4√3

c)

4

d)

8

56.

In this 30-60-90 triangle, what is the length of the long leg?

a)

6√2

b)

3√3

c)

12

d)

6√3

57.

What is b in this 30-60-90 triangle?

a)

b=3.5√3

b)

b = 3.5

c)

b = 7

d)

b = 7√3

58.

Find x.

a)

10

b)

10√3

c)

10√2

d)

20

59.

Find x.

a)

22

b)

11√3

c)

11√2

d)

11

60.

Find a.

a)

12

b)

24

c)

24√3

d)

16

61.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

62.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

63.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

64.

What is the length of x in this picture?

a)

45

b)

5√2

c)

90

d)

5

65.

What is the length of y in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

66.

Which is the length of v in this 30-60-90 triangle?

a)

$4\sqrt{3}$

b)

4

c)

8

d)

$4\sqrt{2}$

67.

What is the length of the short leg of this 30-60-90 triangle?

a)

6

b)

$\frac{6}{\sqrt{3}}$

c)

3

d)

$\frac{6}{\sqrt{2}}$

68.

What is x in this 30-60-90 triangle?

a)

x = 6

b)

x = 3√2

c)

x = 3√3

d)

x = 3√3

69.

What is y in this 30-60-90 triangle?

a)

$y=6$

b)

$y=3\sqrt{2}$

c)

$y=3\sqrt{3}$

d)

$y=\frac{3}{\sqrt{3}}$

70.

What is a in this 30-60-90 triangle?

a)

a = 7√3

b)

a = 7√2

c)

a = 14

d)

a = 14√3

71.

What is the measure of side b?

a)

5

b)

10√2

c)

$\frac{10}{\sqrt{2}}$

d)

10√3

72.

What is the length of y in this triangle?

a)

14

b)

$7\sqrt{3}$

c)

3.5

d)

$\frac{7}{\sqrt{3}}$

73.

What is the length of x in this triangle?

a)

14

b)

$7\sqrt{3}$

c)

3.5

d)

$\frac{14}{\sqrt{3}}$

74.

In this isosceles triangle, what is the length of x?

a)

8√2

b)

$\frac{8}{\sqrt{2}}$

c)

16

d)

8

75.

In this 30-60-90 triangle, what is the length of the hypotenuse?

a)

4√2

b)

4√3

c)

4

d)

8

76.

In this 30-60-90 triangle, what is the length of the long leg?

a)

6√2

b)

3√3

c)

12

d)

6√3

77.

What is b in this 30-60-90 triangle?

a)

b=3.5√3

b)

b = 3.5

c)

b = 7

d)

b = 7√3

78.

Does a triangle with these side lengths exist?
15, 12, 9

a)

Yes

b)

No

c)

I don't know.

79.

Can the sides of a triangle have lengths 3, 8, and 9?

a)

Yes

b)

No

80.

Can the sides of a triangle have lengths 3, 4, and 9?

a)

Yes

b)

No

81.

Can the sides of a triangle have lengths 4, 11, and 13?

a)

Yes

b)

No

82.

What is a possible third side to a triangle with side lengths of 13 and 4?

a)

9

b)

12

c)

8

d)

5

83.

What is a possible third side to a triangle with side lengths of 5 and 5?

a)

9

b)

10

c)

11

d)

12

84.

Name the largest angle in this triangle.

a)

∠D

b)

∠E

c)

∠F

85.

Name the smallest angle in this triangle.

a)

∠A

b)

∠B

c)

∠C

86.

The longest side of a triangle would be located where on a triangle?

a)

Across from the smallest angle

b)

Across from the largest angle

c)

Cannot tell.

d)

Adjacent to the smallest side.

87.

The smallest angle would be located where in a triangle?

a)

Across from the smallest side.

b)

Across from the largest side

c)

Cannot tell

88.

Where would the shortest side of a triangle be located?

a)

Across from the smallest angle in the triangle.

b)

Across from the largest angle in the triangle?

c)

Cannot tell.

89.

Where would the largest angle of a triangle be located?

a)

Across from the longest side.

b)

Across from the shortest side

c)

I need more information to get an answer.

90.

Determine what type (if any) of a triangle would have the following side lengths:

4, 6, 15

a)

acute

b)

obtuse

c)

right

d)

not a triangle

91.

Determine what type (if any) of a triangle would have the following side lengths:

4, 6, 7

a)

acute

b)

obtuse

c)

right

d)

not a triangle

92.

Determine what type (if any) of a triangle would have the following side lengths:

4, 6, 8

a)

acute

b)

obtuse

c)

right

d)

not a triangle

93.

Determine what type (if any) of a triangle would have the following side lengths:

10, 18, 40

a)

acute

b)

obtuse

c)

right

d)

not a triangle

94.

Determine what type (if any) of a triangle would have the following side lengths:

21, 36, 39

a)

acute

b)

obtuse

c)

right

d)

not a triangle

95.

Determine what type (if any) of a triangle would have the following side lengths:

20, 21, 25

a)

acute

b)

obtuse

c)

right

d)

not a triangle

96.

Determine what type (if any) of a triangle would have the following side lengths:

12, 16, 21

a)

acute

b)

obtuse

c)

right

d)

not a triangle

97.

Identify the shortest side measure.

a)

QP

b)

QM

c)

MP

98.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

99.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

100.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

101.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

102.

Can the following side measures form a triangle?
3, 5, 8

a)

Yes

b)

No

103.

The Pythagorean Theorem is
a² + b³= c⁴

a)

false

b)

true

104.

Would a triangle with these side lengths be a right triangle?
4, 5, 6

a)

Yes

b)

No

105.

Which of the following does not represent the lengths of the sides of a triangle?

a)

2 cm, 6 cm, 7 cm

b)

5 cm, 2 cm, 5 cm

c)

5 cm, 5 cm, 8 cm

d)

3 cm, 10 cm, 15 cm

106.

If the longest side of the triangle was 10. Then the two shorter sides must have a sum that is ....?

a)

any length

b)

equal to 10

c)

greater than 10

d)

less than 10

107.

Name the longest side of a right triangle.

a)

leg a

b)

leg b

c)

leg

d)

hypotenuse

108.

a² + b² = c^{2
a = 9 b = 40}

a)

c = 41

b)

c = 65

c)

c = 25

d)

c = 5

109.

Will these three sides form a triangle?

a)

yes

b)

no

110.

Will these line segments form a triangle?

a)

yes

b)

no

111.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

112.

Sides a and b are called legs.

a)

true

b)

false

113.

Level 1

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

114.

Level 3

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

115.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

116.

Level 1

If a right triangle has side lengths 6, 6.7 and 3, which side is the hypotenuse?

a)

6

b)

6.7

c)

3

d)

15.7

e)

None of them

117.

Determine the length of the missing side.

a)

7

b)

8

c)

17

d)

23

118.

what is the formula for finding the hypotnuse?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

119.

What is the length of x?

a)

5

b)

7

c)

8

d)

25

120.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

121.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

122.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

123.

_{^{Find the missing side}}

a)

37

b)

17.66

c)

6

d)

312

124.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

125.

_{^{Find the missing side}}

a)

29.2

b)

20

c)

400

d)

10

126.

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

127.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

128.

Find the length of the missing side.

a)

48 in.

b)

52 in.

c)

16 in.

d)

24 in.

129.

The pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

130.

√121

a)

11

b)

12

c)

21

d)

121

131.

√144

a)

12

b)

4

c)

36

d)

6

132.

Simplify:
√100

a)

1

b)

10

c)

10²

d)

Already simplified

133.

Simplify:
√45

a)

9√5

b)

3√5

c)

5√9

d)

3√15

134.

Simplify:
√200

a)

10√2

b)

2√10

c)

50√2

d)

2√50

135.

Simplify:
3√16

a)

12

b)

48

c)

√12

d)

3√4

136.

Simplify:
√96

a)

16√6

b)

6√16

c)

9√6

d)

4√6

137.

Simplify √60

a)

2√15

b)

12

c)

4√15

d)

3√5

138.

√125

a)

5√5

b)

25√5

c)

5√25

d)

5√2

139.

√243

a)

3√3

b)

9√3

c)

81√3

d)

3√81

140.

In simplest radical form,
√80 is equivalent to

a)

16√5

b)

2√20

c)

4√5

d)

8√5

141.

In simplest radical form,
√75 is equivalent to

a)

25√3

b)

25√3

c)

5√3

d)

3√5

142.

√1

a)

1

b)

2

c)

10

d)

100

143.

√16

a)

4

b)

8

c)

16

d)

64

144.

Simplify the following radical: √32

a)

3√2

b)

4√8

c)

16√2

d)

4√2

145.

√48

a)

4√2

b)

6√3

c)

4√3

d)

4√2

146.

Simplify the following radical: √150

a)

5√15

b)

5√2

c)

5√6

d)

15√5

147.

√169

a)

√13

b)

13

148.

Simplify

a)

9

b)

√9

c)

3√9

d)

can't simplify

Sides of Right Triangles

Total questions: 148

Worksheet time: 7hrs 24mins

Similar Resources on Wayground