Question

Find x A. 22√2 B. 22 C. 11√3/3 D. 11√3

Answer 1

Answer

$22\sqrt{2}$

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.

$sin(45)=\frac{11}{Y}$ , Because sin(x)= op/hip

$cos(60)=\frac{Y}{x}$ , Because con(x)=ad/hip

Having this equations, we can solve the system and find x

$Y=\frac{11}{sin(45)} \\Y=cos(60)*x$

we equal Y and solve

$\frac{11}{sin(45)}=cos(60)*x\\ x=\frac{11}{sin(45)*cos(60)} \\x=\frac{11}{\frac{\sqrt{2} }{2} *\frac{1}{2} } \\x=\frac{11}{\frac{\sqrt{2} }{4} } \\x=\frac{44}{\sqrt{2} }$

Then we rationalize

$x=22\sqrt{2}$

Hope you like it!

Answer 2

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.