Answer:
[tex]x = y = 3\sqrt{ 2[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find x and y
The given triangle has 45 degrees as one of its angles, and it is also a right angle triangle.
For this kind of parameter, the opposite = the adjacent
i.e. x = y
Apply Pythagoras theorem
[tex]x^2 + y^2= 6^2[/tex]
Substitute x for y
[tex]y^2 + y^2= 6^2[/tex]
[tex]2y^2= 36[/tex]
Divide by 2
[tex]y^2 = 18[/tex]
Take square root
[tex]y = \sqrt{18[/tex]
[tex]y = \sqrt{9 * 2[/tex]
Split
[tex]y = \sqrt{9} *\sqrt{ 2[/tex]
[tex]y = 3*\sqrt{ 2[/tex]
[tex]y = 3\sqrt{ 2[/tex]
[tex]x = y = 3\sqrt{ 2[/tex]
