Answer:
[tex] \displaystyle 4 \sqrt{13}in [/tex]
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
[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] \displaystyle \implies{c}^{} = \sqrt{ {a }^{2} + {b}^{2} } [/tex]
let a and b be 8 and 12 respectively thus
substitute:
[tex] \displaystyle {c}^{} = \sqrt{ {8 }^{2} + {12}^{2} } [/tex]
simplify squares:
[tex] \displaystyle {c}^{} = \sqrt{ 64 + 14 4} [/tex]
simplify addition:
[tex] \displaystyle {c}^{} = \sqrt{208} [/tex]
by simplifying the redical expression we obtain:
[tex] \displaystyle {c}^{} = 4 \sqrt{13} [/tex]
