Answer C, .6
Remember the acronym SOHCAHTOA. In particular the theee letter we want to look at are CAH. The C means Cosine, aka. Cos, and the A means adjacent, which shares the same meaning as next to, and the H means hypotenuse, which the last two refer to sides of the triangle. Using the acronym CAH, it helps to remember the Cosine ratio Cos(x)=A/H, meaning the cosine of x equals the adjacent side over the hypotenuse, with x being the angle in focus. Once that’s known, we can create a simple equation. In this problem, your x is angle A, the adjacent side measures .6, and the hypotenuse measures .5, which make up every variable we need to solve for x.
Once that’s plugged into the equation described before, we get Cos(A)=.3/.5 (*you may want to put parenthesis around the decimals in the numerator and denominator, I dont recall for sure but that being there or not might give you a different answer, if it does then the answer using parenthesis is right). From here on, because the question only asks for the cosine of a, figuring it out is as simple as simplifying .3 over .5. .3 is 60% or .6 of .5 which makes .6 your answer, which is the way to figure it no calculator.
Happy to use my semester of pre trig and trig to some good.
