Applying Trig Ratios: Real-Life Scenarios in 10th Grade

A ladder is leaning against a wall. If the base of the ladder is 4 feet away from the wall and the ladder makes a 60-degree angle with the ground, how tall is the wall?

• 8 feet

• 3 feet

• 4√3 feet (approximately 6.93 feet)

• 5 feet

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 30 degrees, how tall is the tree?

• 3.5 meters

• 7.2 meters

• 5.77 meters

• 10 meters

A ramp is built to allow wheelchair access. If the ramp rises 1 meter over a horizontal distance of 5 meters, what is the angle of elevation of the ramp?

• 11.31 degrees

• 30 degrees

• 15 degrees

• 5 degrees

A surveyor is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, how tall is the building?

• 50 meters

• 75 meters

• 100 meters

• 150 meters

A kite is flying at a height of 30 meters. If the string makes a 40-degree angle with the ground, how long is the string?

• 46.15 meters

• 35 meters

• 60 meters

• 25.5 meters

A person is standing 50 meters away from a fountain. If they look up at an angle of 60 degrees to see the top of the fountain, how tall is the fountain?

• 86.6 meters

• 120 meters

• 30 meters

• 50 meters

A boat is anchored 200 meters from the shore. If a line from the boat to a point on the shore makes a 30-degree angle with the water, how deep is the water at that point?

• 75 meters

• 115.47 meters

• 50 meters

• 200 meters

A flagpole casts a shadow of 15 feet. If the angle of elevation from the tip of the shadow to the top of the flagpole is 35 degrees, how tall is the flagpole?

• 12 feet

• 8 feet

• 10.5 feet

• 5 feet

A construction worker is using a crane to lift a beam. If the crane is positioned 12 feet away from the base of the beam and the angle of elevation to the beam is 50 degrees, how high is the beam?

• 12.00 feet

• 14.30 feet

• 18.75 feet

• 10.50 feet

A cyclist is riding up a hill that has a 25-degree incline. If the cyclist travels 200 meters along the hill, how much vertical distance have they gained?

• 200 meters

• 120 meters

• 50 meters

• 84.52 meters