Remark In order to solve for the Cos(x), you need to find the missing side. You can do that by finding the Sin(x) first and then the Cos of x or you can just use the Pythagorean theorem. I'm going to do the latter.
Formula a^2 + b^2 = c^2
Givens a = ??? b = 32 c = 58
Sub and solve a^2 = ??? b^2 = 1024 c^2 = 3364
a^2 + 32^2 = 58^2 1024 + a^2 = 3364 Subtract 1024 from both sides. a^2 = 3364 - 1024 a^2 = 2340 Take the square root of both sides. sqrt(a^2) = sqrt(2340) Break a into its prime factors. a = sqrt(2 * 2 * 5 * 3 * 3 * 13)
Rule For every pair of equal factors, one can be brought outside the root sign and the other is discarded. a = 2 * 3 * sqrt(5*13) a = 6 sqrt(65)
The cos of an angle = opposite / hypotenuse. Cos(x) = 6*sqrt(65) / 58 <<<<< This should be the answer If you are offered choices, you should list them
Another choice would be 6*8.0623 / 58 = 0.8340 <<<<< Answer
LN and KM intersect and are in the same rectangle, which makes them the same line essentially. Set 49 equal to 6x+16 and then solve to get x by itself.
