Exploring Triangles: Side Lengths & Angles in Real Life

A ladder is leaning against a wall. The foot of the ladder is 4 feet away from the wall, and the ladder is 10 feet long. What is the height at which the ladder touches the wall?

• 7.5 feet

• 10 feet

• Approximately 9.17 feet

• 8 feet

A triangular park has sides measuring 30 meters, 40 meters, and 50 meters. Determine if this triangle is a right triangle and find the angles of the triangle.

• Yes, it is a right triangle. Angles are approximately 36.87°, 53.13°, and 90°.

• Yes, it is a right triangle. Angles are approximately 45°, 45°, and 90°.

• Yes, it is a right triangle. Angles are approximately 30°, 60°, and 90°.

• No, it is not a right triangle. Angles are 30°, 60°, and 90°.

A kite is flying at a height of 15 meters. The string makes an angle of 30 degrees with the ground. How long is the string?

• 35 meters

• 25 meters

• 20 meters

• 30 meters

A triangular garden has one angle measuring 60 degrees and the side opposite that angle is 10 meters long. If the other two sides are equal, what are their lengths?

• 8 meters

• 10 meters

• 15 meters

• 12 meters

A triangular piece of land has one angle measuring 45 degrees and the adjacent side is 20 meters long. Calculate the length of the opposite side.

• 10√2 meters (approximately 14.14 meters)

• 5√2 meters (approximately 7.07 meters)

• 20√2 meters (approximately 28.28 meters)

• 15 meters

A roof is shaped like a triangle. The base of the roof is 12 feet, and the height from the base to the peak is 5 feet. What is the area of the roof?

• 30 square feet

• 40 square feet

• 24 square feet

• 15 square feet

In a right triangle, one angle measures 35 degrees, and the side opposite this angle is 7 meters. Calculate the length of the hypotenuse.

• 12.14 meters

• 9.8 meters

• 15.7 meters

• 10.5 meters

A triangular swimming pool has sides of lengths 8 meters, 15 meters, and 17 meters. Calculate the angles of the triangle.

• A ≈ 45°, B ≈ 45°, C ≈ 90°

• A ≈ 60°, B ≈ 30°, C ≈ 90°

• A ≈ 20°, B ≈ 70°, C ≈ 90°

• Angles: A ≈ 30°, B ≈ 53.13°, C = 90°

A flagpole casts a shadow of 10 feet when the angle of elevation of the sun is 60 degrees. How tall is the flagpole?

• 15 feet

• 20 feet

• 5 feet

• 10√3 feet (approximately 17.32 feet)

A triangular plot of land has one angle measuring 90 degrees, and the lengths of the two legs are 6 meters and 8 meters. Calculate the length of the hypotenuse.

• 8 meters

• 12 meters

• 14 meters

• 10 meters