Mastering 30-60-90 Triangles: Side Lengths & Areas

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

• 6 feet

• 10 feet

• 4√3 feet

• 8 feet

A triangular park has one angle measuring 30 degrees and the adjacent side measuring 12 meters. What is the length of the opposite side?

• 10.50 meters

• 8.25 meters

• 6.93 meters

• 5.12 meters

A 30-60-90 triangle has a short leg of 5 cm. What is the length of the long leg and the hypotenuse?

• Long leg: 5 cm, Hypotenuse: 5√3 cm

• Long leg: 10 cm, Hypotenuse: 5√3 cm

• Long leg: 5√3 cm, Hypotenuse: 10 cm

• Long leg: 10√3 cm, Hypotenuse: 5 cm

A roof is designed in the shape of a 30-60-90 triangle. If the height of the roof is 10 feet, what is the area of the roof?

• 35 square feet

• 28.87 square feet

• 15 square feet

• 20 square feet

A triangular garden has a base of 8 meters and a height of 4√3 meters. What type of triangle is it, and what is its area?

• The triangle is acute and its area is 32 square meters.

• The triangle is right and its area is 12 square meters.

• The triangle is obtuse and its area is 24 square meters.

• The triangle is obtuse and its area is 16√3 square meters.

A 30-60-90 triangle is inscribed in a circle with a radius of 10 cm. What are the lengths of the sides of the triangle?

• 8 cm, 8√3 cm, 16 cm

• 10 cm, 10√3 cm, 20 cm

• 10 cm, 15 cm, 25 cm

• 5 cm, 5√3 cm, 10 cm

A right triangle has a height of 9 inches and a base of 9√3 inches. What is the area of the triangle?

• 81 inches

• 40.5√3

• 40.5

• 27√3

If the hypotenuse of a 30-60-90 triangle is 18 cm, what are the lengths of the other two sides?

• Shorter leg: 8 cm, Longer leg: 14 cm

• Shorter leg: 9 cm, Longer leg: 9√3 cm (approximately 15.59 cm)

• Shorter leg: 6 cm, Longer leg: 12 cm

• Shorter leg: 10 cm, Longer leg: 15 cm

A triangular window has a base of 5 feet and a height of 5√3 feet. What is the area of the window?

• 10 square feet

• 5√3 square feet

• 12.5√3 square feet

• 25 square feet

A 30-60-90 triangle is used in a construction project. If the short leg measures 7 meters, what is the area of the triangle?

• 28 square meters

• 49 square meters

• 42.43 square meters

• 35 square meters