Question

write your own steps: 45 - 45 - 90
in 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: x
3
√7
x
x
step #
work

Explanation:

Step1: Apply Pythagorean theorem

For a right - isosceles triangle (45 - 45 - 90), if the legs are of length \(a\), and the hypotenuse is \(x\), by the Pythagorean theorem \(a^{2}+a^{2}=x^{2}\). Given \(a = \sqrt{7}\), we have \((\sqrt{7})^{2}+(\sqrt{7})^{2}=x^{2}\).

Step2: Simplify the equation

\((\sqrt{7})^{2}=7\), so \(7 + 7=x^{2}\), which means \(x^{2}=14\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle (a non - negative quantity), \(x=\sqrt{14}\).

Answer:

\(x = \sqrt{14}\)