Real-Life Trigonometry: Calculate Heights and Angles

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?

• 14.3 feet

• 18.2 feet

• 10.5 feet

• 12.0 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?

• 8.2 meters

• 12.1 meters

• 3.5 meters

• 5.77 meters

A surveyor measures a 45-degree angle from a point on the ground to the top of a hill. If the distance from the point to the base of the hill is 100 meters, how high is the hill?

• 50 meters

• 150 meters

• 200 meters

• 100 meters

A boat is anchored 50 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?

• 25 meters

• 15 meters

• 30 meters

• 40 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?

• 2.50 meters

• 3.14 meters

• 4.00 meters

• 1.71 meters

A person stands 30 meters away from a building and measures the angle of elevation to the top of the building as 40 degrees. How tall is the building?

• 35 meters

• 25.22 meters

• 20 meters

• 15.5 meters

A kite is flying at an angle of 70 degrees from the ground. If the string of the kite is 100 meters long, how high is the kite above the ground?

• 93.97 meters

• 100 meters

• 70 meters

• 80 meters

A cyclist is riding up a hill that has a 15-degree incline. If the cyclist travels 200 meters along the hill, how much vertical distance have they gained?

• 30 meters

• 100 meters

• 51.76 meters

• 75 meters

A flagpole casts a shadow of 12 feet when the angle of elevation of the sun is 45 degrees. How tall is the flagpole?

• 20 feet

• 10 feet

• 15 feet

• 12 feet

A construction worker needs to determine the angle of elevation to the top of a crane from a point 15 meters away. If the crane is 10 meters tall, what is the angle of elevation?

• 33.69 degrees

• 45 degrees

• 25 degrees

• 60 degrees