SOHCAHTOA Applications: Real-Life Angle Problems

A ladder leans against a wall forming a 75-degree angle with the ground. If the base of the ladder is 4 feet away from the wall, how tall is the wall?

• 12.0 feet

• 18.2 feet

• 10.5 feet

• 14.3 feet

A tree casts a shadow of 10 meters when the angle of elevation of the sun is 30 degrees. How tall is the tree?

• 3.5 meters

• 7.2 meters

• 10 meters

• 5.77 meters

A ramp is built at a 20-degree angle to the ground. If the ramp is 5 meters long, how high does it rise?

• 1.71 meters

• 3.14 meters

• 2.50 meters

• 4.00 meters

A surveyor measures a 45-degree angle of elevation to the top of a building from a point 30 meters away. How tall is the building?

• 15 meters

• 45 meters

• 60 meters

• 30 meters

A kite is flying at an angle of 60 degrees from the ground. If the string is 15 meters long, how high is the kite above the ground?

• 10.5 meters

• 15 meters

• 12.99 meters

• 8.7 meters

A boat is anchored 50 meters from the shore. If the angle of elevation to the top of a lighthouse is 40 degrees, how tall is the lighthouse?

• 35 meters

• 55 meters

• 42.75 meters

• 30 meters

A person stands 12 meters away from a building and measures the angle of elevation to the top of the building as 35 degrees. How tall is the building?

• 12.0 meters

• 8.4 meters

• 5.2 meters

• 10.5 meters

A flagpole casts a shadow of 8 meters when the angle of elevation of the sun is 25 degrees. How tall is the flagpole?

• 5.0 meters

• 4.2 meters

• 3.7 meters

• 2.5 meters

A construction worker needs to determine the height of a crane that makes a 70-degree angle with the ground and is 20 meters long. What is the height of the crane?

• 15.5 meters

• 22.3 meters

• 10.0 meters

• 18.79 meters

A cyclist is riding up a hill that makes a 15-degree angle with the horizontal. If the cyclist travels 100 meters up the hill, how much vertical distance have they covered?

• 50.00 meters

• 30.00 meters

• 10.00 meters

• 25.88 meters