By using the Pythagorean Theorem \(\displaystyle a^2+b^2=c^2\), you find the correct answer of \(\displaystyle 5.8in\). 

This is done by plugging in \(\displaystyle 3=a\), and \(\displaystyle 5=b\), since \(\displaystyle c\) was described as the hypotenuse. This gives us:

\(\displaystyle 3^2 + 5^2 = c^2\)

\(\displaystyle 9 + 25 = c^2\)

\(\displaystyle 34 = c^2\)

\(\displaystyle \sqrt{}34 = c\)

\(\displaystyle 5.8=c\)

To solve, simply use the Pythagorean Theorem.

The hypotenuse is the c value in the equation and the two smaller leg lengths are a and b.

Let,

\(\displaystyle \\a=10 \\b=3\)

thus,

\(\displaystyle \\c=\sqrt{a^2+b^2}\\c=\sqrt{10^2+3^2}\\c=\sqrt{100+9}\\c=\sqrt{109}\).

To find the diagonal of a rectangle recall that the diagonal will create a triangle where the width and length are legs of the triangle and the diagonal is the hypotenuse.

To solve, simple use the Pythagorean Theorem and solve for the hypotenuse, which will be the diagonal of the rectangle.

Thus,

\(\displaystyle c=\sqrt{a^2+b^2}=\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}\)

The Pythagorean Theorem states that:

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

Because we know that \(\displaystyle a\) and \(\displaystyle b\) are both \(\displaystyle 10 cm\), we can plug those in to find \(\displaystyle c\):

\(\displaystyle 10^2+10^2=c^2\)

\(\displaystyle 100+100=c^2\)

\(\displaystyle 200=c^2\)

\(\displaystyle c=\sqrt{200}=\sqrt{100}\times \sqrt{2} = 10\sqrt{2}\)

Therefore, the triangle's hypotenuse is \(\displaystyle 10\sqrt{2}cm\).

The formula for Pythagorean Theorem is, \(\displaystyle A^2 + B^2 = C^2\)

C is the hypotenuse and A and B are the other two sides. To begin Pythagorean Theorem the order of A and B does not matter.

If A is 3 and B is 4 then,

\(\displaystyle 3^2 + 4^2 = C^2\)

\(\displaystyle 9 + 16 = C^2\)

\(\displaystyle 25 = C^2\)

You must find C and not c squared. Therefore to get rid of the squared you must do the opposite of squaring something, which is the square root of something. 

\(\displaystyle \sqrt{25} = \sqrt{C^2}\)

\(\displaystyle 5 = C\)

5 inches

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of \(\displaystyle a\) and \(\displaystyle b\),

\(\displaystyle \text{Hypotenuse}^2=a^2+b^2\)

Take the square root of both sides to find the length of the hypotenuse.

\(\displaystyle \text{Hypotenuse}=\sqrt{a^2+b^2}\)

Plug in the given values to find the length of the hypotenuse.

\(\displaystyle \text{Hypotenuse}=\sqrt{10^2 + 4^2}=\sqrt{116}\)

Simply:

\(\displaystyle \sqrt{4}\cdot\sqrt{29}\)

\(\displaystyle 2\sqrt{29}\)

This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that \(\displaystyle a^2+b^2=c^2\) 

 \(\displaystyle 15^2 + 20^2 = c^2\) 

\(\displaystyle 225+400=c^2\)

\(\displaystyle 625=c^2\)

\(\displaystyle 25=c\)

We can find any one missing side of a right triangle with the Pythagorean theorem. 

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

\(\displaystyle 19^2+20^2=c^2\)

\(\displaystyle 361+400=c^2\)

Simplify and take the square root of both sides:

\(\displaystyle \boldsymbol{c=27.6in}\)

To find the length of the hypotenuse, we will use the Pythagorean Theorem

\(\displaystyle a^2+b^2=c^2\).  

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.  

So, first we must square the values of the given sides of the triangle.  

\(\displaystyle 3^2=9\) 

and 

\(\displaystyle 18^2=324\).  

Next, we must add these two solutions to get \(\displaystyle 333\).  

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal: 

\(\displaystyle \sqrt{333}\approx18.248\).

To find the length of the hypotenuse, we will use the Pythagorean Theorem

\(\displaystyle a^2+b^2=c^2\).  

In this formula, c represents the hypotenuse whereas a and b represent the base and height of the right triangle.  

So, first we must square the values of the given sides of the triangle.  

\(\displaystyle 14^2=196\) 

and 

\(\displaystyle 16^2=256\).  

Next, we must add these two solutions to get \(\displaystyle 452\).  

The hypotenuse will be the square root of this number, so using our calculator we can estimate the length of the hypotenuse to be the decimal: 

\(\displaystyle \sqrt{452}\approx21.26\).