Discovering Right Triangles with the Pythagorean Theorem

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. Is the triangle formed by the ladder, the wall, and the ground a right triangle?

• Yes, it is a right triangle.

• No, it is a scalene triangle.

• Yes, it is an isosceles triangle.

• No, it is an obtuse triangle.

A rectangular garden has a length of 10 meters and a width of 6 meters. If you want to plant a diagonal path from one corner to the opposite corner, how long will the path be?

• 11.66 meters

• 10.5 meters

• 12 meters

• 9 meters

A right triangle has one leg measuring 9 cm and the other leg measuring 12 cm. What is the length of the hypotenuse?

• 13 cm

• 15 cm

• 17 cm

• 10 cm

A 15-foot tall tree casts a shadow that is 9 feet long. If you draw a right triangle using the height of the tree and the length of the shadow, what is the distance from the top of the tree to the end of the shadow?

• 15 feet

• 20 feet

• 9 feet

• 17.44 feet

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

• 10 cm

• 8 cm

• 15 cm

• 12 cm

A baseball diamond is a square with each side measuring 90 feet. If you run from home plate to second base, how far do you run?

• 90 feet

• 90√2 feet

• 180 feet

• 45√2 feet

A ramp is built to help wheelchair access. If the ramp is 4 feet high and 3 feet long at the base, what is the length of the ramp?

• 6 feet

• 4 feet

• 5 feet

• 3 feet

A right triangle has angles of 90 degrees, 45 degrees, and 45 degrees. If one leg measures 7 cm, what is the length of the hypotenuse?

• 5 cm

• 10 cm

• 7 cm

• 7√2 cm

A right triangle has a base of 8 inches and a height of 15 inches. Calculate the length of the hypotenuse.

• 12 inches

• 10 inches

• 20 inches

• 17 inches

A kite is flying at a height of 30 meters, and the string makes a 60-degree angle with the ground. If the string is 40 meters long, how far is the kite from the point directly below it on the ground?

• 10 meters

• 35 meters

• 20 meters

• 25 meters