Trigonometry Triumphs: Right Triangle Word Problems

A ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall, and the ladder reaches a height of 8 feet on the wall. What is the length of the ladder?

A right triangle has one leg measuring 5 cm and an angle of 30 degrees opposite to it. What is the length of the other leg?

A tree casts a shadow that is 10 meters long. If the angle of elevation from the tip of the shadow to the top of the tree is 45 degrees, how tall is the tree?

A ramp is built to help wheelchair access. If the ramp rises 3 feet over a horizontal distance of 4 feet, what is the angle of elevation of the ramp?

A kite is flying at a height of 50 meters. If the string makes an angle of 60 degrees with the ground, how far is the kite from the point directly below it on the ground?

A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?

A person is standing 20 meters away from a building. If they look up at an angle of 30 degrees to see the top of the building, how tall is the building?

A right triangle has an angle of 45 degrees and a hypotenuse of 10 cm. What is the length of each leg of the triangle?

A flagpole is 15 feet tall. If the angle of elevation from a point 20 feet away from the base of the flagpole is measured, what is the angle of elevation?

A right triangle has one leg measuring 12 inches and an angle of 60 degrees opposite to it. What is the length of the hypotenuse?