Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

What are the values of x and y?

What Are The Values Of X And Y class=

Sagot :

Based on AA Theorem, which says that if the two given angles of both triangles are equal, then they are similar, in this case, triangle ADB and triangle BDC are similar.  

If two triangles are similar, that means their side length are proportional.

Let us first solve for x:

   [tex]\frac{BD}{DC} =\frac{AD}{DB} \\\frac{9}{x} =\frac{12}{9} \\12x = 81\\x = 6.75\\\\[/tex]

Now using the pythagorean theorem, we get that

   [tex]y^{2} =x^{2} +9^2 = 6.75^2+9^2=126.5625\\y = \sqrt{156.5625} \\y=11.25[/tex]

So x = 6.75 and y = 11.25

Hope that helps!