+0  
 
0
40
1
avatar

Determine the value of a:

 Apr 19, 2020
 #1
avatar+367 
+2

Hi guest!

 

So for this problem, we can connect WY so that we have 2 right triangles, \(\triangle WXY \text { and } \triangle WYZ\)

(Just in case you don't know why \(\triangle WYZ\) is a right triangle, it's because \(\triangle WXY\) is a 45-45-90 triangle (since it has equal legs) and 135-45=90.)

 

First, let's find WY. Triangle WXY is a right triangle, so using the Pythagorean theorem, \(WY=4\sqrt{2}\)

 

Now we know the 1 leg and the hypotenuse of \(\triangle WYZ\)! From here, we can just use the Pythagorean theorem. 

\(a^2+(4\sqrt2)^2=9^2\)

\(a^2+32=81\)

\(a^2=49\)

\(\boxed{a=7}\)

 

I hope this helped you, guest!

:)

 Apr 19, 2020

29 Online Users

avatar
avatar