Answer:
[tex]x =\sqrt 5[/tex]
[tex]y = \sqrt{5[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Solve for x
Considering angle 45 degrees, we have:
[tex]\cos(45) = \frac{y}{\sqrt{10}}[/tex] --- cosine formula i.e. adj/hyp
Solve for y
[tex]y = \sqrt{10} * \cos(45)[/tex]
In radical form, we have:
[tex]y = \sqrt{10} * \frac{1}{\sqrt 2}[/tex]
[tex]y = \sqrt{10/2}[/tex]
[tex]y = \sqrt{5[/tex]
To solve for x, we make use of Pythagoras theorem
[tex]x^2 + y^2 = (\sqrt{10})^2[/tex]
[tex]x^2 + y^2 =10[/tex]
Substitute for y
[tex]x^2 + (\sqrt 5)^2 =10[/tex]
[tex]x^2 + 5 =10[/tex]
Collect like terms
[tex]x^2 =10-5[/tex]
[tex]x^2= 5[/tex]
Solve for x
[tex]x =\sqrt 5[/tex]
