Recall the Pythagorean Theorem for a right triangle:

\(\displaystyle a^2+b^2=c^2\)

Since the missing side corresponds to side \(\displaystyle b\), rewrite the Pythagorean Theorem and solve for \(\displaystyle b\).

\(\displaystyle b^2=c^2-a^2\)

\(\displaystyle b=\sqrt{c^2-a^2}\)

Now, plug in values of \(\displaystyle c\) and \(\displaystyle a\) into a calculator to find the length of side \(\displaystyle b\). Round to \(\displaystyle 2\) decimal places.

\(\displaystyle b=\sqrt{25^2-10^2}=\sqrt{525}=22.91\)

Recall the Pythagorean Theorem for a right triangle:

\(\displaystyle a^2+b^2=c^2\)

Since the missing side corresponds to side \(\displaystyle b\), rewrite the Pythagorean Theorem and solve for \(\displaystyle b\).

\(\displaystyle b^2=c^2-a^2\)

\(\displaystyle b=\sqrt{c^2-a^2}\)

Now, plug in values of \(\displaystyle c\) and \(\displaystyle a\) into a calculator to find the length of side \(\displaystyle b\). Round to \(\displaystyle 2\) decimal places.

\(\displaystyle b=\sqrt{25^2-12^2}=\sqrt{481}=21.93\)

Recall the Pythagorean Theorem for a right triangle:

\(\displaystyle a^2+b^2=c^2\)

Since the missing side corresponds to side \(\displaystyle b\), rewrite the Pythagorean Theorem and solve for \(\displaystyle b\).

\(\displaystyle b^2=c^2-a^2\)

\(\displaystyle b=\sqrt{c^2-a^2}\)

Now, plug in values of \(\displaystyle c\) and \(\displaystyle a\) into a calculator to find the length of side \(\displaystyle b\). Round to \(\displaystyle 2\) decimal places.

\(\displaystyle b=\sqrt{25^2-15^2}=\sqrt{400}=20\)

Recall the Pythagorean Theorem for a right triangle:

\(\displaystyle a^2+b^2=c^2\)

Since the missing side corresponds to side \(\displaystyle b\), rewrite the Pythagorean Theorem and solve for \(\displaystyle b\).

\(\displaystyle b^2=c^2-a^2\)

\(\displaystyle b=\sqrt{c^2-a^2}\)

Now, plug in values of \(\displaystyle c\) and \(\displaystyle a\) into a calculator to find the length of side \(\displaystyle b\). Round to \(\displaystyle 2\) decimal places.

\(\displaystyle b=\sqrt{18^2-3^2}=\sqrt{315}=17.75\)

Recall the Pythagorean Theorem for a right triangle:

\(\displaystyle a^2+b^2=c^2\)

Since the missing side corresponds to side \(\displaystyle b\), rewrite the Pythagorean Theorem and solve for \(\displaystyle b\).

\(\displaystyle b^2=c^2-a^2\)

\(\displaystyle b=\sqrt{c^2-a^2}\)

Now, plug in values of \(\displaystyle c\) and \(\displaystyle a\) into a calculator to find the length of side \(\displaystyle b\). Round to \(\displaystyle 2\) decimal places.

\(\displaystyle b=\sqrt{18^2-7^2}=\sqrt{275}=16.58\)

Recall the Pythagorean Theorem for a right triangle:

\(\displaystyle a^2+b^2=c^2\)

Since the missing side corresponds to side \(\displaystyle b\), rewrite the Pythagorean Theorem and solve for \(\displaystyle b\).

\(\displaystyle b^2=c^2-a^2\)

\(\displaystyle b=\sqrt{c^2-a^2}\)

Now, plug in values of \(\displaystyle c\) and \(\displaystyle a\) into a calculator to find the length of side \(\displaystyle b\). Round to \(\displaystyle 2\) decimal places.

\(\displaystyle b=\sqrt{18^2-9^2}=\sqrt{243}=15.59\)

Recall the Pythagorean Theorem for a right triangle:

\(\displaystyle a^2+b^2=c^2\)

Since the missing side corresponds to side \(\displaystyle b\), rewrite the Pythagorean Theorem and solve for \(\displaystyle b\).

\(\displaystyle b^2=c^2-a^2\)

\(\displaystyle b=\sqrt{c^2-a^2}\)

Now, plug in values of \(\displaystyle c\) and \(\displaystyle a\) into a calculator to find the length of side \(\displaystyle b\). Round to \(\displaystyle 2\) decimal places.

\(\displaystyle b=\sqrt{18^2-6^2}=\sqrt{288}=16.97\)

Recall the Pythagorean Theorem for a right triangle:

\(\displaystyle a^2+b^2=c^2\)

Since the missing side corresponds to side \(\displaystyle b\), rewrite the Pythagorean Theorem and solve for \(\displaystyle b\).

\(\displaystyle b^2=c^2-a^2\)

\(\displaystyle b=\sqrt{c^2-a^2}\)

Now, plug in values of \(\displaystyle c\) and \(\displaystyle a\) into a calculator to find the length of side \(\displaystyle b\). Round to \(\displaystyle 2\) decimal places.

\(\displaystyle b=\sqrt{17^2-8^2}=\sqrt{225}=15\)

To find the length of the side x, we must use the Pythagorean Theorem

\(\displaystyle a^2+b^2=c^2\).  

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.  

So, when we plug the given values into the formula, the equation looks like 

\(\displaystyle 4^2+b^2=5^2\) 

which can be simplified to 

\(\displaystyle 16+b^2=25\).  

Next, solve for b and we get a final answer of 

\(\displaystyle b=\sqrt{9}=3\).  

This particular example is a Pythagorean triple, or a right triangle with 3 whole number values, so it is a good one to remember.

To find the length of the side x, we must use the Pythagorean Theorem

\(\displaystyle a^2+b^2=c^2\).  

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.  

So, when we plug the given values into the formula, the equation looks like 

\(\displaystyle 9^2+b^2=41^2\) 

which can be simplified to 

\(\displaystyle 81+b^2=1681\).  

Next, solve for b and we get a final answer of 

\(\displaystyle b=\sqrt{1600}=40\).  

This particular example is a Pythagorean triple, or a right triangle with 3 whole number values, so it is a good one to remember.