Right Triangle Sides & Pythagorean Challenges for Grade 8

A ladder is leaning against a wall. The foot of the ladder is 4 feet away from the wall, and the ladder reaches a height of 3 feet on the wall. Is the ladder forming a right triangle with the wall and the ground?

• No, the ladder is vertical against the wall.

• Yes, the ladder is forming a right triangle with the wall and the ground.

• No, the ladder is leaning at an angle of 45 degrees.

• Yes, but the ladder is too short to reach the wall.

A right triangle has one leg measuring 6 cm and the other leg measuring 8 cm. What is the length of the hypotenuse?

• 12 cm

• 10 cm

• 8 cm

• 14 cm

A triangular park has a right angle at one corner. If one leg of the triangle is 12 meters long and the other leg is 16 meters long, what is the length of the hypotenuse?

• 20 meters

• 24 meters

• 18 meters

• 22 meters

A ramp is built to help wheelchair access. If the ramp is 5 feet long and rises 3 feet high, how far is the base of the ramp from the wall?

• 2 feet

• 6 feet

• 3.5 feet

• 4 feet

A right triangle has a hypotenuse of 10 inches and one leg measuring 6 inches. What is the length of the other leg?

• 10 inches

• 8 inches

• 4 inches

• 6 inches

A soccer field is rectangular, and a diagonal line is drawn from one corner to the opposite corner. If the length of the field is 50 meters and the width is 30 meters, what is the length of the diagonal?

• 58.31 meters

• 55.00 meters

• 45.00 meters

• 60.00 meters

A right triangle is formed by a tree and the ground. If the tree is 15 feet tall and the distance from the base of the tree to the point where the top of the tree touches the ground is 9 feet, is this a right triangle?

• No, this does not form a right triangle.

• Yes, this forms a right triangle.

• The tree is 9 feet tall, making it a right triangle.

• The distance from the tree to the ground is irrelevant.

A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Calculate the length of the other leg using the Pythagorean theorem.

• 10 cm

• 14 cm

• 8 cm

• 12 cm

A construction worker needs to find the height of a building. He stands 20 meters away from the base of the building and measures the angle of elevation to the top of the building as 60 degrees. Can you find the height of the building using right triangle properties?

• 50 meters

• 25 meters

• 40 meters

• 34.64 meters

A right triangle has legs measuring 7 inches and 24 inches. What is the area of the triangle?

• 84 square inches

• 72 square inches

• 100 square inches

• 56 square inches