Question

What is cos (x)? A) 48/58 B) 58/48 C) 26/58 D) 58/26

Answer 1

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