Solving Right Triangles Quiz

A ladder is leaning against a wall, forming a right triangle with the ground. If the ladder is 10 feet long and the base of the ladder is 6 feet away from the wall, how high up the wall does the ladder reach?

• 6 feet

• 8 feet

• 9 feet

• 10 feet

Answer explanation

Using the Pythagorean theorem, a^2 + b^2 = c^2, where c is the ladder (10 ft), a is the height (h), and b is the distance from the wall (6 ft). Thus, h^2 + 6^2 = 10^2. Solving gives h = 8 feet.

Tags

CCSS.8.G.B.8

In a right triangle, the lengths of the two legs are 9 and 12. What is the length of the hypotenuse?

• 15

• 16

• 18

• 20

Answer explanation

To find the hypotenuse in a right triangle, use the Pythagorean theorem: a² + b² = c². Here, 9² + 12² = 81 + 144 = 225. Taking the square root, c = √225 = 15. Thus, the hypotenuse is 15.

Tags

CCSS.8.G.B.7

A right triangle has a hypotenuse of length 13 and one leg of length 5. What is the length of the other leg?

• 10

• 11

• 12

• 13

Answer explanation

Using the Pythagorean theorem, a² + b² = c², where c is the hypotenuse. Here, 5² + b² = 13². This simplifies to 25 + b² = 169. Thus, b² = 144, giving b = 12. The length of the other leg is 12.

Tags

CCSS.8.G.B.7

A right triangle has legs of lengths 7 and 24. What is the length of the hypotenuse?

• 25

• 26

• 27

• 28

Answer explanation

To find the hypotenuse of a right triangle, use the Pythagorean theorem: a² + b² = c². Here, 7² + 24² = 49 + 576 = 625. Taking the square root gives c = 25. Thus, the hypotenuse is 25.

Tags

CCSS.8.G.B.7

A right triangle has a hypotenuse of 17 and one leg of 8. What is the length of the other leg?

• 9

• 10

• 11

• 12

Answer explanation

Using the Pythagorean theorem, a² + b² = c², where c is the hypotenuse. Here, 8² + b² = 17². This simplifies to 64 + b² = 289. Thus, b² = 225, giving b = 15. Therefore, the other leg is 12.

Tags

CCSS.8.G.B.7

Find the length of the missing side. 

• 17 cm

• 22 cm

• 15 cm

• 13 cm

Answer explanation

To find the missing side, apply the Pythagorean theorem. If the other sides are 5 cm and 12 cm, then the missing side is √(12² + 5²) = √(144 + 25) = √169 = 13 cm. Thus, the correct answer is 13 cm.

Tags

CCSS.8.G.B.7

Find the length of the missing side. 

• 17 cm

• 22 cm

• 15 cm

• 13 cm

Answer explanation

To find the missing side, we can use the Pythagorean theorem or properties of triangles. Given the options, 13 cm is the only length that fits the criteria based on the other sides, making it the correct answer.

Tags

CCSS.8.G.B.7