Find the value of x. Write your answer in simplest form.

x = (9/2)√2

Step-by-step explanation:

The ratio of leg x to the hypotenuse 9 is equal to the cosine of 45 degrees:

cos 45 degrees = x/9

To find the value of x, multiply both sides of this equation by 9, obtaining 9*cos 45 degrees, which comes out to x =9(1/√2).  Rationalizing the denominator, we get x = (9/2)√2

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: