Mastering Triangle Properties: 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

• 10 feet

• 14 feet

• 12 feet

A rectangular garden has a length of 10 meters and a width of 24 meters. What is the length of the diagonal of the garden?

• 26 meters

• 20 meters

• 30 meters

• 22 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?

• 12 cm

• 14 cm

• 10 cm

• 8 cm

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

• 120 feet

• 60 feet

• 100 feet

• 90√2 feet (approximately 127.28 feet)

A right triangle has a base of 12 inches and a height of 16 inches. What is the length of the hypotenuse?

• 15 inches

• 20 inches

• 22 inches

• 18 inches

A 5-meter tall tree casts a shadow of 4 meters. If you stand 3 meters away from the base of the tree, how tall is the triangle formed by the tree, the ground, and the line from the top of the tree to the tip of the shadow?

• 7.2 meters

• 6.5 meters

• 8.75 meters

• 10 meters

A ramp is built to connect a loading dock that is 3 feet high to the ground. If the ramp is 4 feet long, how far is the base of the ramp from the wall of the loading dock?

• 1.5 feet

• 3.5 feet

• 4.5 feet

• Approximately 2.65 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?

• 12 cm

• 6 cm

• 8 cm

• 10 cm

A kite is flying at a height of 40 meters. If the string of the kite is 50 meters long, how far is the kite from the point on the ground directly below it?

• 20 meters

• 30 meters

• 35 meters

• 45 meters

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

• 12 cm

• 10 cm

• 15 cm

• 8 cm