Real-world examples explaining the Pythagorean Theorem (a² + b² = c²)

📚 Quick Study Guide

• 📐 The Pythagorean Theorem applies only to right triangles.
• 📏 It states that the sum of the squares of the two shorter sides (legs, $a$ and $b$) is equal to the square of the longest side (hypotenuse, $c$).
• 🔢 The formula is: $a^2 + b^2 = c^2$.
• 💡 If you know the lengths of two sides of a right triangle, you can find the length of the third side using this theorem.
• 🗺️ Applications include navigation, construction, and surveying.

🤔 Practice Quiz

1. What type of triangle does the Pythagorean Theorem apply to?
   1. Acute triangle
   2. Obtuse triangle
   3. Right triangle
   4. Equilateral triangle
2. A ladder is leaning against a wall. The base of the ladder is 3 feet from the wall, and the ladder reaches 4 feet up the wall. How long is the ladder?
   1. 5 feet
   2. 7 feet
   3. 12 feet
   4. 25 feet
3. A rectangular garden is 8 meters long and 6 meters wide. What is the length of the diagonal of the garden?
   1. 10 meters
   2. 14 meters
   3. 48 meters
   4. 100 meters
4. A baseball diamond is a square with sides of 90 feet. What is the distance from home plate to second base?
   1. 90 feet
   2. 127.28 feet
   3. 180 feet
   4. 8100 feet
5. A ship sails 12 miles east and then 5 miles north. How far is the ship from its starting point?
   1. 7 miles
   2. 13 miles
   3. 17 miles
   4. 60 miles
6. What is the length of the hypotenuse of a right triangle if the lengths of the legs are 7 cm and 24 cm?
   1. 17 cm
   2. 25 cm
   3. 31 cm
   4. 625 cm
7. A telephone pole is 40 feet tall. A wire is stretched from the top of the pole to a point on the ground 30 feet from the base of the pole. How long is the wire?
   1. 10 feet
   2. 50 feet
   3. 70 feet
   4. 100 feet