Find the Length of b

 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 5 \\ a = & 4 \end{matrix} & \begin{matrix} A = \\ B = \\ C = & 90 \end{matrix} \end{matrix}$

Step 1

Use the Pythagorean theorem to find the unknown side. In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (the two sides other than the hypotenuse).

$a^{2} + b^{2} = c^{2}$

Step 2

Solve the equation for $b$ .

$b = \sqrt{c^{2} - a^{2}}$

Step 3

Substitute the actual values into the equation.

$b = \sqrt{{(5)}^{2} - {(4)}^{2}}$

Step 4

Raise $5$ to the power of $2$ .

$b = \sqrt{25 - {(4)}^{2}}$

Step 5

Raise $4$ to the power of $2$ .

$b = \sqrt{25 - 1 \cdot 16}$

Step 6

Multiply $- 1$ by $16$ .

$b = \sqrt{25 - 16}$

Step 7

Subtract $16$ from $25$ .

$b = \sqrt{9}$

Step 8

Rewrite $9$ as $3^{2}$ .

$b = \sqrt{3^{2}}$

Step 9

Pull terms out from under the radical, assuming positive real numbers.

$b = 3$

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