Question

Please help me and show ur work (multiple choice)m

Answer 1

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.

$\frac{4 \sqrt{2} }{ \sqrt{2} } = 4$

To check our work let use the pythagorean theorem, since it a right angle

${4}^{2} + {4}^{2} =h {}^{2}$

$16 + 16 = {h}^{2}$

$32 = {h}^{2}$

$\sqrt{32}$

$\sqrt{16} \times \sqrt{2}$

$4 \times \sqrt{2}$

$4 \sqrt{2}$

so it is correct.