Real-Life Applications of SOHCAHTOA: Trig Word Problems

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 tall is the ladder?

• 7 meters

• 5 meters

• 3 meters

• 4√3 meters (approximately 6.93 meters)

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

• 8.2 meters

• 5.77 meters

• 12.0 meters

• 3.5 meters

A ramp is built at a 15-degree angle to the ground. If the ramp is 5 meters long, how high does it rise?

• 1.30 meters

• 6.0 meters

• 4.0 meters

• 2.5 meters

A kite is flying at an angle of 45 degrees with a string length of 20 meters. How high is the kite above the ground?

• 25 meters

• 10 meters

• 17.32 meters

• 14.14 meters

A building is 50 meters tall. From a point on the ground, the angle of elevation to the top of the building is 30 degrees. How far is the point from the base of the building?

• 50√3 meters

• 50 meters

• 100 meters

• 25 meters

A person stands 30 meters away from a flagpole and measures the angle of elevation to the top of the flagpole as 60 degrees. How tall is the flagpole?

• 70 meters

• 30 meters

• 40 meters

• 51.96 meters

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 water, how deep is the water at that point?

• 30 meters

• 57.74 meters

• 100 meters

• 45 meters

A 12-meter tall tower casts a shadow of 8 meters. What is the angle of elevation of the sun?

• 45 degrees

• 56.31 degrees

• 30 degrees

• 75 degrees

A cyclist rides up a hill that has a 20-degree incline. If the cyclist travels 100 meters along the hill, how much vertical distance have they gained?

• 40.0 meters

• 50.5 meters

• 25.0 meters

• 34.2 meters

A 5-meter tall statue is viewed from a distance of 12 meters. What is the angle of elevation from the viewer's eyes to the top of the statue?

• 15.75 degrees

• 30.00 degrees

• 10.50 degrees

• 22.62 degrees