Question

Find the length of the missing side.

Answer 1

Answer:

$\displaystyle 4 \sqrt{13}in$

Step-by-step explanation:

we are given a right angle triangle and we want to figure out the missing hypotenuse in order to do so we can consider using Pythagoras theorem given by

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

$\displaystyle \implies{c}^{} = \sqrt{ {a }^{2} + {b}^{2} }$

let a and b be 8 and 12 respectively thus

substitute:

$\displaystyle {c}^{} = \sqrt{ {8 }^{2} + {12}^{2} }$

simplify squares:

$\displaystyle {c}^{} = \sqrt{ 64 + 14 4}$

simplify addition:

$\displaystyle {c}^{} = \sqrt{208}$

by simplifying the redical expression we obtain:

$\displaystyle {c}^{} = 4 \sqrt{13}$

Answer 2

Answer:

14.4 inches

Step-by-step explanation:

Use the Pythagorean theorem: $a^{2} + b^{2}$

So, this will be: $8^{2} + 12^{2} = c^{2}$

By simplifying we get:

c = $\sqrt{208}$

The missing side is: 14.4 (rounded to the tenth)