Mastering 30-60-90 Triangles: Side Length Challenges

A ladder leans against a wall, forming a 30-degree angle with the ground. If the base of the ladder is 6 feet from the wall, how tall is the ladder?

• 3 feet

• 4 feet

• 5 feet

• 2√3 feet (approximately 3.46 feet)

A triangular park has one angle measuring 60 degrees and the side opposite this angle is 10 meters long. What are the lengths of the other two sides?

• 8.0 meters and 12.0 meters

• 7.5 meters and 9.2 meters

• The lengths of the other two sides are approximately 5.77 meters and 11.55 meters.

• 6.5 meters and 13.0 meters

A 30-60-90 triangle is formed by a rope tied to a tree. If the length of the rope (the hypotenuse) is 12 feet, what is the length of the side opposite the 30-degree angle?

• 8 feet

• 4 feet

• 6 feet

• 10 feet

A ramp is built to help wheelchair access, forming a 30-degree angle with the ground. If the ramp is 15 feet long, how high does it reach?

• 10 feet

• 12 feet

• 5 feet

• 7.5 feet

In a right triangle, one angle measures 30 degrees and the hypotenuse is 20 inches. What is the length of the side opposite the 60-degree angle?

• 20 inches

• 5√3 inches

• 10√3 inches

• 10 inches

A triangular garden has a height of 8 feet and forms a 60-degree angle with the ground. What is the length of the base of the triangle?

• 3.464 feet

• 4.618 feet

• 5.000 feet

• 6.928 feet

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

• 10 meters

• 7.5 meters

• 8.66 meters

• 6 meters

A kite is flying at a height of 10 meters, forming a 30-degree angle with the ground. How far is the kite from the point directly below it on the ground?

• 10 meters

• 10√3 meters

• 15√2 meters

• 5 meters

A triangular roof has a height of 12 feet and forms a 60-degree angle with the base. What is the length of the base of the roof?

• 10 feet

• 6 feet

• 8√3 feet

• 4√3 feet

A 30-60-90 triangle is used in a design. If the longer leg measures 10 cm, what is the length of the hypotenuse?

• 15 cm

• 18 cm

• 20 / √3 or approximately 11.55 cm

• 12 cm