Answer:
A
Step-by-step explanation:
This is a 45 45 90 triangle since it has 45 and a 90 degree angle so using triangle interior theorem, the third angle is 45.
The legs of a 45 45 90 triangle are congruent so only A is right.
But since you want the work
The length of the hypotenuse in 45 45 90 triangle is sqr root of 2 times more than both of the legs so
let divide sqr root of 2 by the hypotenuse to find the legs.
[tex] \frac{4 \sqrt{2} }{ \sqrt{2} } = 4[/tex]
To check our work let use the pythagorean theorem, since it a right angle
[tex] {4}^{2} + {4}^{2} =h {}^{2} [/tex]
[tex]16 + 16 = {h}^{2} [/tex]
[tex]32 = {h}^{2} [/tex]
[tex] \sqrt{32} [/tex]
[tex] \sqrt{16} \times \sqrt{2} [/tex]
[tex]4 \times \sqrt{2} [/tex]
[tex]4 \sqrt{2} [/tex]
so it is correct.
