Pythagorean Theorem worksheet featuring nine right triangles with missing side lengths to be calculated.

To find the missing lengths, we use the Pythagorean theorem: $a^2 + b^2 = c^2$.
* $a$ and $b$ are the legs (the sides touching the right angle).
* $c$ is the hypotenuse (the longest side, opposite the right angle).

If you are looking for a leg, the formula is: $\text{Leg} = \sqrt{\text{Hypotenuse}^2 - \text{Other Leg}^2}$.
If you are looking for the hypotenuse, the formula is: $\text{Hypotenuse} = \sqrt{\text{Leg}_1^2 + \text{Leg}_2^2}$.

Here are the step-by-step solutions for each problem, rounded to the nearest tenth:

1) Find BC
* Hypotenuse ($AC$) = 15, Leg ($AB$) = 12.
* $BC = \sqrt{15^2 - 12^2}$
* $BC = \sqrt{225 - 144}$
* $BC = \sqrt{81}$
* $BC = 9$

2) Find PQ
* Hypotenuse ($PQ$) is unknown. Legs are 7 and 2.
* $PQ = \sqrt{7^2 + 2^2}$
* $PQ = \sqrt{49 + 4}$
* $PQ = \sqrt{53}$
* $PQ \approx 7.3$

3) Find UW
* Hypotenuse ($VW$) = 9, Leg ($UV$) = 6.
* $UW = \sqrt{9^2 - 6^2}$
* $UW = \sqrt{81 - 36}$
* $UW = \sqrt{45}$
* $UW \approx 6.7$

4) Find XZ
* Hypotenuse ($XZ$) is unknown. Legs are 14 and 3.
* $XZ = \sqrt{14^2 + 3^2}$
* $XZ = \sqrt{196 + 9}$
* $XZ = \sqrt{205}$
* $XZ \approx 14.3$

5) Find EF
* Hypotenuse ($EG$) = 10, Leg ($FG$) = 8.
* $EF = \sqrt{10^2 - 8^2}$
* $EF = \sqrt{100 - 64}$
* $EF = \sqrt{36}$
* $EF = 6$

6) Find JL
* Hypotenuse ($JL$) is unknown. Legs are 13 and 17.
* $JL = \sqrt{13^2 + 17^2}$
* $JL = \sqrt{169 + 289}$
* $JL = \sqrt{458}$
* $JL \approx 21.4$

7) Find MN
* Hypotenuse ($MN$) is unknown. Legs are 8 and 16.
* $MN = \sqrt{8^2 + 16^2}$
* $MN = \sqrt{64 + 256}$
* $MN = \sqrt{320}$
* $MN \approx 17.9$

8) Find ST
* Hypotenuse ($SU$) = 7, Leg ($TU$) = 1.
* $ST = \sqrt{7^2 - 1^2}$
* $ST = \sqrt{49 - 1}$
* $ST = \sqrt{48}$
* $ST \approx 6.9$

9) Find CE
* Hypotenuse ($CE$) is unknown. Legs are 7 and 11.
* $CE = \sqrt{7^2 + 11^2}$
* $CE = \sqrt{49 + 121}$
* $CE = \sqrt{170}$
* $CE \approx 13.0$

Final Answer:
1) BC = 9
2) PQ = 7.3
3) UW = 6.7
4) XZ = 14.3
5) EF = 6
6) JL = 21.4
7) MN = 17.9
8) ST = 6.9
9) CE = 13.0