Answer
[tex]22\sqrt{2}[/tex]
Step-by-step explanation:
First we gave a name to the side that is common for both triangles, can be Y for example.
Using trigonometric functions we can make a relationship between the two angles that we have and the magnitud of the side.
[tex]sin(45)=\frac{11}{Y} \\[/tex] , Because sin(x)= op/hip
[tex]cos(60)=\frac{Y}{x}[/tex] , Because con(x)=ad/hip
Having this equations, we can solve the system and find x
[tex]Y=\frac{11}{sin(45)} \\Y=cos(60)*x[/tex]
we equal Y and solve
[tex]\frac{11}{sin(45)}=cos(60)*x\\ x=\frac{11}{sin(45)*cos(60)} \\x=\frac{11}{\frac{\sqrt{2} }{2} *\frac{1}{2} } \\x=\frac{11}{\frac{\sqrt{2} }{4} } \\x=\frac{44}{\sqrt{2} }\\[/tex]
Then we rationalize
[tex]x=22\sqrt{2}[/tex]
Hope you like it!
Answer:
A. 22√2.
Step-by-step explanation:
The diagonal of the small triangle = 11√2 ( because it is a 45-45-90 triangle).
cos 60 = 11√2 / x
x = 11√2 / cos 60
= 11√2 / 1/2
= 22√2.
