Question

Find the value of x. (Hint: Use a trigonometric ratio or what you know about the lengths of sides in special right triangles.)

Answer 1

Tan 45 = perpendicular/base 

1= 9 / x

x= 9 units

Answer 2

Since all triangles have a sum of 180° and this is a right triangle with a 90 and a 45.  The other angle must be 45.  Since the side opposite the 45 is 9 units long, and the x is opposite the same angle it must also have a length of 9 units.

x=9