30-60-90 Triangles: Solving Real-World Problems

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 high does the ladder reach on the wall?

• 2√3 feet

• 3 feet

• 4√3 feet

• 5 feet

A triangular park has one angle measuring 60 degrees and the opposite side is 12 meters long. What is the length of the side opposite the 30-degree angle?

• 4 meters

• 10 meters

• 8 meters

• 6 meters

A 30-60-90 triangle is formed by a ramp. If the height of the ramp is 10 feet, how long is the base of the ramp?

• 12.5 feet

• 7.5 feet

• 8.66 feet

• 5.77 feet

A kite is flying at a height of 15 meters. If the angle of elevation from the ground to the kite is 30 degrees, how far is the kite from the person on the ground?

• 20√3 meters

• 10 meters

• 15 meters

• 15√3 meters

A triangular garden has a 60-degree angle. If the shortest side measures 5 meters, what is the length of the longest side?

• 6.3 meters

• 4.5 meters

• 7.1 meters

• 5.77 meters

A 30-60-90 triangle is used to design a roof. If the height of the roof is 8 feet, what is the length of the base of the triangle?

• 8√3 / 3 feet

• 8 feet

• 4 feet

• 16 feet

A flagpole casts a shadow that forms a 30-degree angle with the ground. If the shadow is 10 feet long, how tall is the flagpole?

• 10 feet

• 8.2 feet

• 5.77 feet

• 3.5 feet

In a 30-60-90 triangle, if the length of the hypotenuse is 18 cm, what is the length of the side opposite the 30-degree angle?

• 9 cm

• 12 cm

• 6 cm

• 15 cm

A construction worker needs to build a ramp with a 60-degree angle. If the ramp is 20 feet long, how high will it rise?

• 10 feet

• 17.32 feet

• 20 feet

• 15 feet

A triangular window has a 30-degree angle and a height of 4 feet. What is the length of the base of the window?

• 6√2 feet

• 4√3 feet

• 5 feet

• 3 feet