Abrace for a shelf has the shape of a right triangle. its hypotense is 16 incges long and the two legs are equal in length. how long arr the legs of the triangle

We use trigonometry because we know an angle and a side length. 

We are looking for one of the sides that isn't the hypotenuse:
As illustrated by the picture I made below:

We know both unknown angles will be 45 degrees, as there are 180 degrees in a triangle, we know the triangle is a right angle triangle (has 90 degrees) so, (180-90)/2 = 45

Using SOH CAH TOA, short for :  SIN- OH  COS- AH  TAN- OA

We are looking for the one with H, as we know what H is.
I am picking "SIN- OH", but we could use "COS- AH"

The formula for this is: Sin(angle) = O/H
We substitute the angle (45) and the length for H (16)

Sin(45)= O/16 <- rearrange it
Sin(45)*16= O <- Solve in the calculator
13.6145 (4 DP)= O
The legs = O

The legs have a length of "13.6145 (4 DP)" each 

11/36 is .305 repeating