Examples of finding a missing leg using Pythagorean Theorem

📚 Quick Study Guide

• 📐 The Pythagorean Theorem applies to right triangles only.
• 📝 The formula is: $a^2 + b^2 = c^2$, where 'a' and 'b' are the legs, and 'c' is the hypotenuse.
• ➕ To find a missing leg (a or b), rearrange the formula: $a^2 = c^2 - b^2$ or $b^2 = c^2 - a^2$.
• 💡 Remember to take the square root at the end to find the actual length of the leg.
• 📏 Units are important! Make sure all measurements are in the same unit before applying the theorem.

Practice Quiz

1. A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
   1. 8 cm
   2. 12 cm
   3. 18 cm
   4. 24 cm
2. A ladder is leaning against a wall. The ladder is 10 feet long, and the base of the ladder is 6 feet from the wall. How high up the wall does the ladder reach?
   1. 4 feet
   2. 8 feet
   3. 12 feet
   4. 16 feet
3. A rectangular garden is 12 meters long and its diagonal is 15 meters. What is the width of the garden?
   1. 3 meters
   2. 6 meters
   3. 9 meters
   4. 18 meters
4. What is the length of the missing leg of a right triangle with a hypotenuse of 25 inches and one leg measuring 7 inches?
   1. 18 inches
   2. 23 inches
   3. 24 inches
   4. 26 inches
5. A baseball diamond is a square with sides of 90 feet. What is the distance from home plate to second base (the diagonal)? (Round to the nearest foot)
   1. 90 feet
   2. 127 feet
   3. 135 feet
   4. 180 feet
6. A TV screen is 36 inches wide and has a diagonal of 45 inches. What is the height of the TV screen?
   1. 9 inches
   2. 27 inches
   3. 30 inches
   4. 39 inches
7. A right triangle has a hypotenuse of 17 m and one leg of 8 m. Find the length of the other leg.
   1. 9 m
   2. 15 m
   3. 25 m
   4. 35 m