Applying Cosine: Real-Life Trigonometry Challenges

A tree casts a shadow of 15 meters when the angle of elevation of the sun is 30 degrees. How tall is the tree?

• 5 meters

• 8.66 meters

• 10 meters

• 12 meters

A ladder leans against a wall, forming a 60-degree angle with the ground. If the base of the ladder is 4 meters from the wall, how long is the ladder?

• 6 meters

• 8 meters

• 12 meters

• 10 meters

A boat is anchored 10 meters from the shore. If the angle of elevation from the boat to the top of a lighthouse is 45 degrees, how tall is the lighthouse?

• 20 meters

• 15 meters

• 5 meters

• 10 meters

A surveyor is standing 50 meters from the base of a hill. If the angle of elevation to the top of the hill is 35 degrees, how tall is the hill?

• 35.01 meters

• 60 meters

• 45 meters

• 25.5 meters

A cable car is suspended from a point 20 meters above the ground. If the cable makes a 30-degree angle with the ground, how far is the cable car from the base of the pole?

• 30√3 meters

• 10 meters

• 20√3 meters

• 20 meters

A person is standing 30 meters away from a building. If they look up at a 60-degree angle to see the top of the building, how tall is the building?

• 40 meters

• 51.96 meters

• 25 meters

• 70 meters

A ramp is built to connect a loading dock that is 1.5 meters high. If the ramp makes a 45-degree angle with the ground, how long is the ramp?

• 2.121 meters

• 1.5 meters

• 2.0 meters

• 3.0 meters

A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground 40 meters away from the kite is 36 degrees, how far is the kite from that point?

• 70 meters

• 40 meters

• 50 meters

• 60 meters

A cyclist is riding on a path that is inclined at an angle of 25 degrees. If the cyclist travels 100 meters along the path, how much vertical distance have they covered?

• 50.00 meters

• 30.00 meters

• 42.26 meters

• 60.00 meters