Right Triangle Challenges: Sides and Angles in Action

A ladder leans against a wall, forming a right triangle. If the base of the ladder is 4 feet from the wall and the ladder is 10 feet long, what is the height at which the ladder touches the wall?

• 9.17 feet

• 10 feet

• 8 feet

• 7.5 feet

In a right triangle, one angle measures 30 degrees and the side opposite this angle is 5 meters long. What is the length of the hypotenuse?

• 12 meters

• 8 meters

• 10 meters

• 6 meters

A tree casts a shadow that is 8 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?

• 8 meters

• 10 meters

• 6 meters

• 12 meters

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

• 30 degrees

• 15 degrees

• 45 degrees

• 24.62 degrees

A right triangle has one angle measuring 60 degrees and the adjacent side is 7 cm long. What is the length of the opposite side?

• 15 cm

• 8.7 cm

• 12.12 cm

• 10.5 cm

A surveyor measures a 50-meter long cable that is anchored to a point on the ground. If the angle between the cable and the ground is 30 degrees, how high is the cable anchored above the ground?

• 40 meters

• 15 meters

• 35 meters

• 25 meters

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

• 14 cm

• 12 cm

• 10 cm

• 8 cm

A kite is flying at a height of 15 meters. If the string makes an angle of 30 degrees with the ground, how long is the string?

• 30 meters

• 35 meters

• 20 meters

• 25 meters

A building is 20 meters tall. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. How far is the point from the base of the building?

• 11.55 meters

• 20 meters

• 8.66 meters

• 15.75 meters

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

• 10 cm

• 20 cm

• 5√2 cm

• 10√2 cm