Exploring Special Right Triangles: Real-Life Applications

A ladder is leaning against a wall, forming a right triangle with the ground. If the ladder is 10 feet long and the base of the ladder is 6 feet from the wall, how high up the wall does the ladder reach?

• 5 feet

• 10 feet

• 12 feet

• 8 feet

A triangular park has one angle measuring 90 degrees, and the two shorter sides are in a ratio of 1:√3. If the shorter side is 4 meters, what is the length of the longest side?

• 10 meters

• 12 meters

• 6 meters

• 8 meters

A 45-45-90 triangle is formed by a triangular roof. If each leg of the triangle is 8 feet long, what is the length of the roof's peak to the base?

• 8 feet

• 8√2 feet

• 16 feet

• 4√2 feet

A right triangle is formed by a ramp leading to a loading dock. If the ramp is 12 feet long and the height of the dock is 9 feet, how far is the base of the ramp from the dock?

• 10 feet

• 5√3 feet

• 4 feet

• 3√7 feet

A right triangle is formed by a tree and the ground. If the tree is 15 feet tall and casts a shadow of 15 feet, what type of special triangle is formed?

• Equilateral triangle

• Scalene triangle

• Obtuse triangle

• Isosceles right triangle

A 30-60-90 triangle is used in a construction project. If the shorter leg is 5 meters, what is the length of the longer leg?

• 8.66 meters

• 10 meters

• 6 meters

• 7.5 meters

A triangular garden has a right angle, with one leg measuring 10 feet and the hypotenuse measuring 26 feet. What is the length of the other leg?

• 22 feet

• 18 feet

• 20 feet

• 24 feet

A right triangle is formed by a kite string and the ground. If the string is 20 feet long and the angle between the string and the ground is 30 degrees, how high is the kite above the ground?

• 10 feet

• 15 feet

• 5 feet

• 25 feet

A 45-45-90 triangle is used in a design. If the hypotenuse is 14√2 inches, what is the length of each leg?

• 10 inches

• 12 inches

• 16 inches

• 14 inches

A right triangle is formed by a flagpole and the ground. If the flagpole is 30 feet tall and the distance from the base of the pole to the point where the top of the pole casts a shadow is 30 feet, what type of triangle is formed?

• Scalene triangle

• Isosceles right triangle

• Equilateral triangle

• Obtuse triangle