# Given a right triangle triangle ABC with C=90^circ, if a=2, c=6, how do you find b?

Nov 5, 2017

$b = 4 \sqrt{2}$

#### Explanation: Using the Pythagorean Theorem,
${a}^{2} + {b}^{2} = {c}^{2}$
$b = \sqrt{{c}^{2} - {a}^{2}}$
$b = \sqrt{{6}^{2} - {2}^{2}}$
$b = 4 \sqrt{2}$

Nov 5, 2017

The side $b$ is $4 \sqrt{2}$ unit.

#### Explanation:

in right triangle Delta ABC , /_C=90^0 , a=2 , c=6 ; c  is

the side opposite to the right angle, so it is hypotenuse,

$a \mathmr{and} b$ are the adjacent sides of the right angle .

We know in right triangle $\Delta A B C , {a}^{2} + {b}^{2} = {c}^{2}$

$\therefore {2}^{2} + {b}^{2} = {6}^{2} \mathmr{and} {b}^{2} = 36 - 4 = 32 \therefore b = \sqrt{32} \mathmr{and} b = 4 \sqrt{2}$

unit. The side $b$ is $4 \sqrt{2}$ unit [Ans]

Nov 5, 2017

$4 \sqrt{2}$

#### Explanation:

Consider the diagram Since this is a right triangle,

We can find the length $b$ by using the Pythagoras theorem

color(blue)(a^2+b^2=c^2

Plugin the values

$\rightarrow {2}^{2} + {b}^{2} = {6}^{2}$

$\rightarrow 4 + {b}^{2} = 36$

$\rightarrow {b}^{2} = 32$

Take the square root of both sides

$\rightarrow \sqrt{{b}^{2}} = \sqrt{32}$

$\rightarrow b = \sqrt{16 \cdot 2}$

color(green)(rArrb=4sqrt2

Hope that helps!!! ☺♣☻