Practice worksheet for calculating missing side lengths in right triangles using the Pythagorean theorem.

To solve the missing side lengths in each right triangle using the Pythagorean theorem, we use the formula:

\[
a^2 + b^2 = c^2
\]

where:
- \( a \) and \( b \) are the legs of the right triangle,
- \( c \) is the hypotenuse (the longest side).

Let's solve each problem step by step.

---

1)

Given:
- One leg = 12 yd
- Hypotenuse = 15 yd
- Missing side = \( x \)

Using the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
\[
x^2 + 12^2 = 15^2
\]
\[
x^2 + 144 = 225
\]
Subtract 144 from both sides:
\[
x^2 = 81
\]
Take the square root of both sides:
\[
x = \sqrt{81} = 9
\]

Answer:
\[
x = 9 \text{ yd}
\]

---

2)

Given:
- One leg = 16 in
- Hypotenuse = 20 in
- Missing side = \( x \)

Using the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
\[
x^2 + 16^2 = 20^2
\]
\[
x^2 + 256 = 400
\]
Subtract 256 from both sides:
\[
x^2 = 144
\]
Take the square root of both sides:
\[
x = \sqrt{144} = 12
\]

Answer:
\[
x = 12 \text{ in}
\]

---

3)

Given:
- One leg = 5 ft
- Other leg = 12 ft
- Missing side = \( x \) (hypotenuse)

Using the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
\[
5^2 + 12^2 = x^2
\]
\[
25 + 144 = x^2
\]
\[
169 = x^2
\]
Take the square root of both sides:
\[
x = \sqrt{169} = 13
\]

Answer:
\[
x = 13 \text{ ft}
\]

---

4)

Given:
- One leg = 8 yd
- Hypotenuse = 10 yd
- Missing side = \( x \)

Using the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
\[
x^2 + 8^2 = 10^2
\]
\[
x^2 + 64 = 100
\]
Subtract 64 from both sides:
\[
x^2 = 36
\]
Take the square root of both sides:
\[
x = \sqrt{36} = 6
\]

Answer:
\[
x = 6 \text{ yd}
\]

---

5)

Given:
- One leg = 18 in
- Hypotenuse = 30 in
- Missing side = \( x \)

Using the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
\[
x^2 + 18^2 = 30^2
\]
\[
x^2 + 324 = 900
\]
Subtract 324 from both sides:
\[
x^2 = 576
\]
Take the square root of both sides:
\[
x = \sqrt{576} = 24
\]

Answer:
\[
x = 24 \text{ in}
\]

---

6)

Given:
- One leg = 36 ft
- Hypotenuse = 65 ft
- Missing side = \( x \)

Using the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
\[
x^2 + 36^2 = 65^2
\]
\[
x^2 + 1296 = 4225
\]
Subtract 1296 from both sides:
\[
x^2 = 2929
\]
Take the square root of both sides:
\[
x = \sqrt{2929} = 54
\]

Answer:
\[
x = 54 \text{ ft}
\]

---

Final Answers:

\[
\boxed{9, 12, 13, 6, 24, 54}
\]