# How do you find the length of the missing side given a=19 b=? c=26?

Jul 3, 2016

$b = 17.74$

#### Explanation:

We need to use the Pythagorean Theorem:

The hypotenuse (c=26) and one of the legs (a=19) are known, so all we have to do is solve for b. We can do that by plugging in our known values:

${19}^{2} + {b}^{2} = {26}^{2}$

${19}^{2}$ or $19 \times 19$ = 361
${26}^{2}$ or $26 \times 26$ = 676

Thus, $361 + {b}^{2} = 676$. Now subtract 361 from both sides of the equation to get ${b}^{2}$ by itself:

$361 + {b}^{2} = 676$
-361 -361

You should end up with:

${b}^{2} = 315$

Next, take the square root of both sides to find b. The square root
(sqrt) is the inverse of the square (${b}^{2}$)

$\sqrt{{b}^{2}} = \sqrt{315}$

Therefore, b = 17.74

You can check your answer by plugging a and c into the equation and solve for b to see if your answer matches the given value of b:

${19}^{2} + {17.74}^{2} = {26}^{2}$