Question

solve for x and z.

x
√5
45°
z

x = 5√2, z = 5
x = √2, z = √5
x = √10, z = √5
x = 5, z = 2√5

Explanation:

Step1: Identify triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the legs are equal. So $z=\sqrt{5}$.

Step2: Use Pythagorean theorem

For a right - triangle with legs $a$ and $b$ and hypotenuse $c$, $a^{2}+b^{2}=c^{2}$. Here $a = z=\sqrt{5}$, $b=\sqrt{5}$, and $c = x$. So $x^{2}=(\sqrt{5})^{2}+(\sqrt{5})^{2}$.
$x^{2}=5 + 5=10$.

Step3: Solve for $x$

Taking the square root of both sides, $x=\sqrt{10}$.

Answer:

$x=\sqrt{10},z=\sqrt{5}$