Section 13.1 - Right Triangle Trigonometry - Solving Right ... - Free Printable

To find the missing side of each right triangle, we use the Pythagorean Theorem:

> a² + b² = c²

Where:
- a and b are the legs (the two shorter sides that form the right angle)
- c is the hypotenuse (the longest side, opposite the right angle)

We’ll solve each problem one by one. If we’re solving for a leg, we rearrange the formula:

> leg = √(hypotenuse² - other leg²)

If we’re solving for the hypotenuse:

> hypotenuse = √(leg₁² + leg₂²)

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Let’s go through each numbered triangle:

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1. Legs: 3 and 4 → Find hypotenuse
→ c = √(3² + 4²) = √(9 + 16) = √25 = 5

2. Leg: 5, Hypotenuse: 13 → Find other leg
→ b = √(13² - 5²) = √(169 - 25) = √144 = 12

3. Legs: 6 and 8 → Find hypotenuse
→ c = √(6² + 8²) = √(36 + 64) = √100 = 10

4. Leg: 7, Hypotenuse: 25 → Find other leg
→ b = √(25² - 7²) = √(625 - 49) = √576 = 24

5. Legs: 5 and 12 → Find hypotenuse
→ c = √(5² + 12²) = √(25 + 144) = √169 = 13

6. Leg: 9, Hypotenuse: 15 → Find other leg
→ b = √(15² - 9²) = √(225 - 81) = √144 = 12

7. Legs: 8 and 15 → Find hypotenuse
→ c = √(8² + 15²) = √(64 + 225) = √289 = 17

8. Leg: 12, Hypotenuse: 20 → Find other leg
→ b = √(20² - 12²) = √(400 - 144) = √256 = 16

9. Legs: 7 and 24 → Find hypotenuse
→ c = √(7² + 24²) = √(49 + 576) = √625 = 25

10. Leg: 10, Hypotenuse: 26 → Find other leg
→ b = √(26² - 10²) = √(676 - 100) = √576 = 24

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All answers are whole numbers — no rounding needed.

Final Answer:
1. 5
2. 12
3. 10
4. 24
5. 13
6. 12
7. 17
8. 16
9. 25
10. 24