SOHCAHTOA in Action: Right Triangles in Real Life

A ladder leans against a wall, forming a right triangle with the ground. If the ladder is 10 feet long and the base is 6 feet from the wall, what is the height at which the ladder touches the wall?

• 9 feet

• 5 feet

• 8 feet

• 7 feet

In a right triangle, the angle of elevation to the top of a tree is 30 degrees, and you are standing 20 meters away from the base of the tree. How tall is the tree?

• 25 meters

• 11.55 meters

• 8 meters

• 15 meters

A ramp is built to allow wheelchair access. If the ramp rises 4 feet over a horizontal distance of 12 feet, what is the angle of elevation of the ramp?

• 30 degrees

• 25 degrees

• 18.43 degrees

• 15 degrees

A surveyor measures a 45-degree angle of elevation to the top of a building from a point 50 meters away. How tall is the building?

• 100 meters

• 70 meters

• 50 meters

• 30 meters

A kite is flying at a height of 30 meters, and the string makes a 60-degree angle with the ground. How long is the string?

• 25√2 meters

• 20√3 meters

• 15 meters

• 30√3 meters

A right triangle has one angle measuring 60 degrees, and the side opposite this angle is 5 cm long. What is the length of the hypotenuse?

• 3.33 cm

• 7.5 cm

• 6.25 cm

• 4.33 cm

You are standing 15 meters from a flagpole. If the angle of elevation to the top of the flagpole is 40 degrees, how tall is the flagpole?

• 8.2 meters

• 12.14 meters

• 15 meters

• 10.5 meters

A boat is anchored 100 meters from the shore. If the angle of elevation from the boat to the top of a cliff is 25 degrees, how high is the cliff?

• 46.63 meters

• 100 meters

• 75 meters

• 30 meters

In a right triangle, if the adjacent side is 8 cm and the angle is 30 degrees, what is the length of the opposite side?

• 5 cm

• 3.5 cm

• 4.618 cm

• 6 cm

A person is looking at a building from a distance of 30 meters. If the angle of elevation to the top of the building is 35 degrees, how tall is the building?

• 18.2 meters

• 30.0 meters

• 21.0 meters

• 15.5 meters