Since the values are the same on both sides the matrix value is a=1
All the numbers in this range can be written as

with

and

. Construct a table like so (see attached; apparently the environment for constructing tables isn't supported on this site...)
so that each entry in the table corresponds to the sum of the tens digit (row) and the ones digit (column). Now, you want to find the numbers whose digits add to perfect squares, which occurs when the sum of the digits is either of 1, 4, 9, or 16. You'll notice that this happens along some diagonals.
For each number that occupies an entire diagonal in the table, it's easy to see that that number

shows up

times in the table, so there is one instance of 1, four of 4, and nine of 9. Meanwhile, 16 shows up only twice due to the constraints of the table.
So there are 16 instances of two digit numbers between 10 and 92 whose digits add to perfect squares.
We'll use the following properties of sine and cosine to prove this:



Then it's just a matter of filling it in...
sin20sin40 * sin60sin80 = 1/2(cos20 - cos60) * 1/2 (cos20 - cos140) =
1/8( cos40 + 1 - cos160 - cos120 - cos40 - cos80 + cos80 + cos200) =
1/8(1 - cos160 - cos120 + cos200) =
1/8(1 - cos160 - cos120 + cos160) =
1/8(1 - cos120 ) = 1/8( 1 + 1/2 ) = 3/16
So this inequality is going to be written as 9(x + 6) > 99
Firstly, you want to foil 9(x + 6), which will look like this: 9x + 54 > 99
Next, subtract 54 on both sides of the equation: 9x > 45
Lastly, divide both sides by 9, and your answer will be x > 5