Exploring 45-45-90 Triangles in Everyday Life

A ladder is leaning against a wall, forming a 45-degree angle with the ground. If the base of the ladder is 4 feet away from the wall, how high up the wall does the ladder reach?

• 8 feet

• 6 feet

• 4 feet

• 2 feet

A square garden has a diagonal path that divides it into two equal triangular sections. If each side of the garden is 10 meters long, what is the length of the diagonal path?

• 5√2 meters

• 20 meters

• 10 meters

• 10√2 meters

A right triangle is formed by a ramp leading to a loading dock. If the ramp makes a 45-degree angle with the ground and is 6 feet long, how high does the ramp rise?

• 6 feet

• 4 feet

• 3√2 feet

• 2√2 feet

A triangular park has two sides that are equal in length and form a 45-degree angle with the ground. If each side is 8 meters long, what is the height of the park at its highest point?

• 4√2 meters

• 5 meters

• 6 meters

• 8√2 meters

A roof is designed in the shape of a 45-45-90 triangle. If the base of the roof is 12 feet wide, what is the height of the roof?

• 6 feet

• 8 feet

• 10 feet

• 4 feet

A right triangle is formed by a tree and the ground. If the tree is 10 feet tall and the angle between the ground and the line from the top of the tree to the ground is 45 degrees, how far is the base of the tree from the point directly below the top of the tree?

• 10 feet

• 5 feet

• 15 feet

• 20 feet

A triangular piece of land has a right angle at one corner and two sides of equal length. If each side measures 5 meters, what is the area of the triangular piece of land?

• 12.5 square meters

• 15 square meters

• 20 square meters

• 10 square meters

A square window has a diagonal that measures 14 inches. What is the length of each side of the window?

• 12 inches

• 8 inches

• 9.9 inches

• 10 inches

A 45-45-90 triangle is used in a design for a triangular flag. If the legs of the triangle are each 3 feet long, what is the length of the hypotenuse?

• 6 feet

• 3√2 feet

• 4 feet

• 3√3 feet

A right triangle is formed by a ramp that is 10 feet long and makes a 45-degree angle with the ground. How high does the ramp rise?

• 7 feet

• 3 feet

• 5√2 feet (approximately 7.07 feet)

• 10 feet