Free Printable Pythagorean Theorem and Special Right Triangles

1.

True or False: The Pythagorean Theorem can be used to solve acute or obtuse triangles.

a)

True

b)

False

2.

Determine the length of the missing side.

a)

7

b)

8

c)

17

d)

23

3.

Name the longest side of a right triangle.

a)

leg a

b)

leg b

c)

leg

d)

hypotenuse

4.

Which equation can be used to solve for "x"?

a)

x² + 15² = 21²

b)

x² – 15² = 21²

c)

15² + 21² = x²

d)

x² + 21² = 15²

5.

Side c on a right triangle is ALWAYS the longest.

a)

True

b)

False

6.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

7.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

8.

^{Find the missing side}

a)

9

b)

41

c)

6.4

d)

3

9.

The slide at a playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. To find the length of the slide, which diagram would I use?

a)

b)

c)

d)

10.

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

a)

44.1 km

b)

59 km

c)

47.8 km

d)

33 km

11.

How far from the base of a house do you need to place a 15' ladder so that is exactly reaches the top of a 12' wall?

a)

9 feet

b)

19.2 feet

c)

81 feet

d)

369 feet

12.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

13.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

14.

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

a)

12 feet

b)

13.9 feet

15.

Level 1

If a right triangle has side lengths 6, 7 and 3, which side is the hypotenuse?

a)

6

b)

7

c)

3

d)

49

e)

9

16.

Level 4

Solve for x.

a)

38.9

b)

40.2

c)

45.6

d)

54

17.

What is the final step in solving this work for c?
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²

a)

Divide both sides by 2

b)

Take the square root of both sides

18.

The Pythagorean Theorem is

a² - b² = c²

a)

false

b)

true

19.

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

a)

Yes

b)

No

20.

Does the set of numbers represent a right triangle?

20, 25, 15

a)

Yes

b)

No

21.

a = 2.1, b = 7.2,
c = 7.5
Is this a right triangle?

a)

yes

b)

no

22.

Do these 3 side lengths form a right triangle?
13, 80, and 81?

a)

yes

b)

no

23.

If a = 9 and b = 7, what is c?

a)

130

b)

12.4

c)

11.4

d)

11

24.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

25.

State if the three sides lengths form an acute, obtuse, or right triangle:
6 mi, 14 mi, 17 mi

a)

acute

b)

obtuse

c)

right

26.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

27.

State if the three sides lengths form an acute, obtuse, or right triangle:
7 in, 11 in, 13 in

a)

acute

b)

obtuse

c)

right

28.

An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?

a)

65 miles

b)

89 miles

c)

45.4 miles

d)

We don't have enough information.

29.

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

a)

7.5 in

b)

12.4 in

c)

13.6 in

d)

14.3 in

30.

The longest side of a right triangle is DIRECTLY ACROSS from the...

a)

right angle.

b)

acute angle.

c)

obtuse angle.

31.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

32.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Isosceles

d)

Obtuse

33.

Find x.

a)

10

b)

10√3

c)

10√2

d)

20

34.

Find x.

a)

22

b)

11√3

c)

11√2

d)

11

35.

Find a.

a)

12

b)

24

c)

24√3

d)

16

36.

Find a.

a)

2√3

b)

2

c)

12

d)

6

37.

Find x.

a)

9

b)

3√3

c)

6

d)

6√3

38.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

39.

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

40.

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

a)

16

b)

8

c)

8√2

d)

√16

41.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

42.

Find the length of m.

a)

4

b)

6

c)

12

d)

2√3

43.

Determine the length of x.

a)

x = 3/2

b)

x = 3

c)

x = 3√3

d)

x = 6

44.

Determine the value of x.

a)

x = 10√2

b)

x = 10

c)

x = 5√3

d)

x = 5√6

45.

Determine the value of x.

a)

x = 8√2

b)

x = 16√2

c)

x = 16

d)

x = 8√6

46.

Determine the value of c.

a)

c = 6√3

b)

c = 12√3

c)

c = 18

d)

c = 18√2

47.

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

48.

I have been given a hypotenuse in this 45-45-90 triangle. How do I find the length of a leg of the triangle?

a)

Multiply by √2

b)

Divide by √2

c)

It's the same length as the hypotenuse.

d)

Divide by 2

49.

I have been given the short leg in this 30-60-90 triangle. How do I find the length of the hypotenuse?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by √3

50.

Which side is the short leg in this 30-60-90 triangle?

a)

4

b)

u

c)

v

51.

I have been given the hypotenuse in this 30-60-90 triangle. How do I find the short leg?

a)

Multiply 6 by 2

b)

Multiply 6 by √3

c)

Divide 6 by 2

d)

Divide 6 by √3

52.

I have been given the long leg in this 30-60-90 triangle. How do I find the short leg?

a)

Multiply 7 by 2

b)

Multiply 7 by √3

c)

Divide 7 by 2

d)

Divide 7 by √3

53.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

54.

Find x. Round to the 10ths place (one decimal place) if necessary.

(a)

55.

What is the height of the TV? Round to the 10ths place (one decimal place) if necessary.

(a)

56.

A ramp on a moving truck makes a $30\degree$ angle with the ground. What is the length of the ramp if it is 5 ft tall? Round to the 10ths place (one decimal place) if necessary.

(a)

57.

Which set of numbers are possible lengths of a right triangle?

a)

I only

b)

I, II, & IV only

c)

III only

d)

I and IV only

58.

What is the length of u and v in this 30-60-90 triangle?

a)

u = 8 v = 4√3

b)

u = 4√2 v = 8

c)

u = 16 v = 8

d)

u = 4√3 v = 8

59.

Find the value of m.

a)

10

b)

10√2

c)

20√2

d)

√2

60.

Find the value of x.

a)

9

b)

2√3

c)

1

d)

3

61.

Find the value of x.

a)

3 sqrt(2)

b)

3

c)

6 sqrt(2)

d)

6

62.

I have been given the hypotenuse in this 30-60-90 triangle. How do I find the short leg?

a)

Multiply 6 by 2

b)

Multiply 6 by √3

c)

Divide 6 by 2

d)

Divide 6 by √3

63.

Find the missing side lengths.

a)

a = 4, b = 4

b)

a = 4, b = 2√2

c)

a = 2√2, b = 4

d)

a = 4, b = 4

64.

Find a.

a)

3

b)

$3\sqrt{3}$

c)

6

d)

$\sqrt{3}$

65.

Find x.

a)

10

b)

$10\sqrt{3}$

c)

$10\sqrt{2}$

d)

20

66.

Which side is the long leg in this 30-60-90 triangle? (not the hypotenuse)

a)

4

b)

u

c)

v

67.

Choose the correct values for x and y in the right triangle.

a)

$x=12$

b)

$x=12\sqrt{2}$

c)

$y\ =\ 24$

d)

$y=12\sqrt{2}$

68.

Choose the correct values for x and y in the right triangle.

a)

$x=14$

b)

$x=7\sqrt{2}$

c)

$y\ =\ 7$

d)

$y=7\sqrt{2}$

69.

Choose the correct values for x and y in the right triangle.

a)

$x=3$

b)

$x=3\sqrt{2}$

c)

$y\ =\ 6$

d)

$y=6\sqrt{2}$

70.

Choose the correct values for x and y in the right triangle.

a)

$x=\frac{11\sqrt{3}}{3}$

b)

$x=11$

c)

$y\ =\ 22$

d)

$y=11\sqrt{3}$

71.

$\sin\theta=$

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{hypotenuse}{opposite}$

c)

$\frac{adjacent}{hypotenuse}$

d)

$\frac{opposite}{adjacent}$

72.

$\cos\theta=$

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{hypotenuse}{adjacent}$

c)

$\frac{adjacent}{hypotenuse}$

d)

$\frac{opposite}{adjacent}$

73.

$\tan\theta=$

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{hypotenuse}{adjacent}$

c)

$\frac{adjacent}{opposite}$

d)

$\frac{opposite}{adjacent}$

74.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

75.

Choose the correct ratio.

a)

cos(33)=x/14

b)

sin(33)=x/14

c)

cos(33)=14/x

d)

sin(33)=14/x

76.

Solve for x. Round to the nearest tenth.

a)

7.5

b)

34.1

c)

14.1

77.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

78.

Find the length of the missing side x...

Round your answer to 1 decimal place.

a)

8.7 cm

b)

10.2 cm

c)

12.3 cm

d)

8.6 cm

79.

Find the length of the missing side x...

Round your answer to 1 decimal place.

a)

10.3 cm

b)

10.2 cm

c)

17.5 cm

d)

8.6 cm

80.

Find the length of the missing side x...

Round your answer to 1 decimal place.

a)

5.7 cm

b)

5.8 cm

c)

17.1 cm

d)

8.6 cm

81.

Find the length of the missing side x...

Round your answer to 1 decimal place.

a)

3.8 cm

b)

28.8 cm

c)

3.9 cm

d)

3.6 cm

82.

Find the length of the missing side x...

Round your answer to 1 decimal place.

a)

8.3 cm

b)

16.7 cm

c)

11.8 cm

d)

8.4 cm

83.

Find the length of the missing side x...

Round your answer to 1 decimal place.

a)

15.1 cm

b)

15.2 cm

c)

10.1 cm

d)

10.2 cm

84.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

85.

a)

44.55

b)

22.69

c)

41.66

d)

38.49

Pythagorean Theorem and Special Right Triangles

Total questions: 85

Worksheet time: 4hrs 29mins

Similar Resources on Wayground