Solving Right Triangle Word Problems: Angles & Context

A ladder leans 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, what is the angle between the ladder and the ground?

• 30 degrees

• 75 degrees

• 90 degrees

• 53.13 degrees

A right triangle has one angle measuring 30 degrees. If the length of the side opposite this angle is 5 meters, what is the length of the hypotenuse?

• 6 meters

• 10 meters

• 12 meters

• 8 meters

A park has a triangular section where one angle is 90 degrees. If one leg of the triangle is 8 meters and the other leg is 6 meters, what is the measure of the angle opposite the 6-meter side?

• 60 degrees

• 36.87 degrees

• 53.13 degrees

• 45 degrees

A ramp is built to help wheelchair access to a building. If the ramp is 12 feet long and rises 5 feet, what is the angle of elevation of the ramp?

• 30 degrees

• 45 degrees

• 15 degrees

• 23.58 degrees

In a right triangle, one angle measures 45 degrees and the hypotenuse is 10 cm long. What is the length of each leg of the triangle?

• 8 cm

• 6 cm

• 5√2 cm

• 7 cm

A right triangle has a height of 9 inches and a base of 12 inches. What is the measure of the angle opposite the height?

• 45 degrees

• 53.13 degrees

• 60 degrees

• 36.87 degrees

A tree casts a shadow that is 15 feet long. If the angle of elevation from the tip of the shadow to the top of the tree is 60 degrees, how tall is the tree?

• 25.98 feet

• 20 feet

• 10 feet

• 30 feet

A right triangle has one angle measuring 70 degrees. If the length of the side adjacent to this angle is 10 cm, what is the length of the hypotenuse?

• 15.00 cm

• 40.00 cm

• 25.00 cm

• 34.64 cm

A kite is flying at a height of 30 meters. If the string makes a 45-degree angle with the ground, how long is the string?

• 40√2 meters

• 30 meters

• 30√2 meters

• 20 meters

A right triangle has one angle measuring 30 degrees and the hypotenuse is 20 meters long. What is the length of the side opposite the 30-degree angle?

• 10 meters

• 5 meters

• 15 meters

• 25 meters