8th Grade Sine and Cosine Challenges in Real-Life Scenarios

A tree casts a shadow of 15 feet. 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? (Use sine)

• 12 feet

• 5 feet

• 7.5 feet

• 10 feet

A ladder leans against a wall, forming a 60-degree angle with the ground. If the base of the ladder is 5 feet from the wall, how long is the ladder? (Use cosine)

• 8 feet

• 15 feet

• 12 feet

• 10 feet

A ramp is built to allow wheelchair access. If the ramp is 10 feet long and rises to a height of 4 feet, what angle does the ramp make with the ground? (Use sine)

• arcsin(0.4)

• arcsin(0.5)

• arcsin(0.6)

• arcsin(0.3)

A kite is flying at a height of 20 meters. If the string makes a 45-degree angle with the ground, how long is the string? (Use sine)

• 25 meters

• 20 meters

• 15 meters

• 20√2 meters

A building is 50 feet tall. From a point 30 feet away from the base of the building, what is the angle of elevation to the top of the building? (Use tangent and then find sine)

• 59.04 degrees

• 30.00 degrees

• 45.67 degrees

• 72.34 degrees

A 12-foot tall flagpole casts a shadow of 9 feet. What is the angle of elevation of the sun? (Use tangent and then find sine)

• 45 degrees

• 60 degrees

• 30 degrees

• 53.13 degrees

A boat is anchored 100 meters from the shore. If a line from the boat to a point on the shore makes a 30-degree angle with the shore, how far is the boat from the point directly across from it on the shore? (Use cosine)

• 86.6 meters

• 70.0 meters

• 100.0 meters

• 50.0 meters

A 25-foot tall tree casts a shadow of 20 feet. What is the angle of elevation of the sun? (Use tangent and then find sine)

• Approximately 30 degrees

• Approximately 75 degrees

• Approximately 51.34 degrees

• Approximately 45 degrees

A person stands 40 feet away from a building and looks up at the top of the building, which is 30 feet tall. What is the angle of elevation? (Use tangent and then find sine)

• 25 degrees

• 50 degrees

• 36.87 degrees

• 45 degrees

A right triangle has one leg measuring 8 cm and an angle of 30 degrees. What is the length of the hypotenuse? (Use sine)

• 14 cm

• 10 cm

• 16 cm

• 12 cm