Right Triangle Challenges: Pythagorean & Side Identification

A ladder leans against a wall, forming a right triangle with the ground. If the base of the ladder is 4 feet from the wall and the ladder is 10 feet long, how high up the wall does the ladder reach?

• 10 feet

• 9.17 feet

• 7.5 feet

• 8 feet

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

• 9 cm

• 8 cm

• 7 cm

• 5 cm

A ramp is built to allow wheelchair access. If the ramp is 12 feet long and rises to a height of 5 feet, how far is the base of the ramp from the wall it is leaning against?

• 12 feet

• 6.5 feet

• 10.91 feet

• 8.5 feet

A triangular park has one side measuring 8 meters and a hypotenuse measuring 10 meters. Calculate the length of the other side of the triangle.

• 4 meters

• 5 meters

• 7 meters

• 6 meters

A right triangle has an angle of 30 degrees and the side opposite this angle measures 5 meters. What is the length of the hypotenuse?

• 6 meters

• 12 meters

• 8 meters

• 10 meters

A tree casts a shadow that is 15 feet long. If the angle of elevation from the tip of the shadow to the top of the tree is 45 degrees, how tall is the tree?

• 25 feet

• 10 feet

• 20 feet

• 15 feet

A right triangle has legs measuring 9 inches and 12 inches. What is the length of the hypotenuse?

• 15 inches

• 14 inches

• 10 inches

• 18 inches

A kite is flying at a height of 30 meters. If the string makes a 60-degree angle with the ground, how long is the string?

• 20√3 meters

• 15 meters

• 30 meters

• 25√2 meters

A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the length of the other leg.

• 6 cm

• 12 cm

• 8 cm

• 10 cm

A construction worker needs to determine the height of a building. He stands 20 meters away from the base and measures the angle of elevation to the top of the building as 30 degrees. How tall is the building?

• 8.25 meters

• 11.55 meters

• 20 meters

• 15.75 meters