Exploring Triangle Properties with Pythagorean Challenges

A ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall, and the ladder reaches a height of 8 feet on the wall. How long is the ladder?

• 8 feet

• 12 feet

• 10 feet

• 5 feet

A rectangular garden has a length of 10 meters and a width of 24 meters. What is the length of the diagonal that stretches from one corner of the garden to the opposite corner?

• 22 meters

• 26 meters

• 20 meters

• 30 meters

A right triangle has one leg that measures 9 cm and a hypotenuse that measures 15 cm. What is the length of the other leg?

• 8 cm

• 14 cm

• 10 cm

• 12 cm

A baseball diamond is a square with each side measuring 90 feet. What is the distance from home plate to second base?

• 45√2 feet

• 180 feet

• 90 feet

• 90√2 feet

A 5-foot tall person is standing 12 feet away from a tree. If the top of the tree is 20 feet high, how far is the top of the tree from the person in a straight line?

• approximately 19.2 feet

• 15 feet

• 30 feet

• 25 feet

A right triangle has angles of 30 degrees and 60 degrees. If the side opposite the 30-degree angle is 5 cm, what is the length of the hypotenuse?

• 8 cm

• 6 cm

• 12 cm

• 10 cm

A ramp is built to help wheelchair access. If the ramp rises 3 feet over a horizontal distance of 4 feet, what is the length of the ramp?

• 4 feet

• 6 feet

• 5 feet

• 7 feet

A kite is flying at a height of 40 meters. If the string is pulled taut and makes a 60-degree angle with the ground, how long is the string?

• 50.00 meters

• 35.50 meters

• 30.00 meters

• 46.19 meters

A swimming pool is rectangular with a length of 15 meters and a width of 20 meters. What is the length of the diagonal across the pool?

• 30 meters

• 25 meters

• 20 meters

• 15 meters

A right triangle has a perimeter of 30 cm. If one leg is 10 cm long, what is the length of the other leg and the hypotenuse?

• Other leg: 8 cm, Hypotenuse: 14 cm

• Other leg: 10 cm, Hypotenuse: 10 cm

• Other leg: 5 cm, Hypotenuse: 15 cm

• Other leg: 7.5 cm, Hypotenuse: 12.5 cm