Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the legs are of equal length and the hypotenuse $c$ is $\sqrt{2}$ times the length of a leg $a$ (i.e., $c = a\sqrt{2}$). Here, the hypotenuse $c = 2.2$ and the leg is $x$.

Step2: Set up the equation

We know that $c=a\sqrt{2}$, so $2.2=x\sqrt{2}$.

Step3: Solve for $x$

We can rewrite the equation as $x=\frac{2.2}{\sqrt{2}}$. Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{2}$: $x=\frac{2.2\sqrt{2}}{2}=1.1\sqrt{2}\approx1.1\times1.414 = 1.5554\approx1.6$.

Answer:

$1.6$