Question

write your own steps: 45 - 45 - 90
on the left is the example from the previous slide. use it as a model for your work on the problem on the right. you will need to copy this symbol at point: ≈.

Explanation:

Step1: Recall the 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, the legs are equal, and the hypotenuse \(x\) is related to the leg \(a\) by the formula \(x = a\sqrt{2}\).

Step2: Substitute the value of the leg

Here, the leg \(a=\sqrt{7}\). So, \(x=\sqrt{7}\times\sqrt{2}\).

Step3: Simplify the expression

Using the property \(\sqrt{m}\times\sqrt{n}=\sqrt{mn}\), we get \(x = \sqrt{7\times2}=\sqrt{14}\).

Answer:

\(x=\sqrt{14}\)