Sohcahtoa Challenges: Sine & Cosine Word Problems

A ladder is leaning against a wall. The foot 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 top of the ladder on the wall?

• 3 feet

• 7 feet

• 5 feet

• 4√3 feet (approximately 6.93 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?

• 10 meters

• 5.77 meters

• 3.5 meters

• 7.2 meters

A ramp is built to allow wheelchair access to a building. If the ramp is 12 feet long and makes a 45-degree angle with the ground, how high does the ramp reach at the building?

• 7√2 feet (approximately 9.90 feet)

• 5 feet

• 10 feet

• 6√2 feet (approximately 8.49 feet)

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

• 20 meters

• 35 meters

• 25 meters

• 30 meters

A surveyor is standing 50 meters away from a building. If the angle of elevation to the top of the building is 40 degrees, how tall is the building?

• 42.75 meters

• 35 meters

• 55 meters

• 30 meters

A boat is anchored 20 meters from a dock. If the angle between the boat and the dock is 60 degrees, how far is the boat from the point directly across from the dock?

• 10 meters

• 5 meters

• 15 meters

• 25 meters

A flagpole casts a shadow of 8 meters long. If the angle of elevation from the tip of the shadow to the top of the flagpole is 45 degrees, how tall is the flagpole?

• 8 meters

• 10 meters

• 12 meters

• 6 meters

A construction worker is using a crane to lift a beam. If the beam is lifted at an angle of 30 degrees and the crane's cable is 25 meters long, how high is the beam lifted?

• 10 meters

• 20 meters

• 15 meters

• 12.5 meters

A person is standing 30 meters away from a building and looking up at the top. If the angle of elevation is 50 degrees, how tall is the building?

• 25 meters

• 50 meters

• 40 meters

• 35.75 meters

A cyclist is riding up a hill that has a 20-degree incline. If the cyclist travels 100 meters along the hill, how high does the cyclist rise?

• 25.0 meters

• 40.0 meters

• 50.0 meters

• 34.2 meters