Question

In a right triangle, if tan x = 1/2 then what is cos x

Answer 1

Answer:

               2√5

cos x = -------------

                   5

Step-by-step explanation:

If tan x = 1/2 then what is cos x?  

Recall that tan x is defined as the quotient sin x / cos x, so that in this case sin x / cos x = 1 / 2 = opp side / adjacent side.  Also, recall that cos x = adj side / hypotenuse.

To determine cos x, we need to find the length of the hypotenuse.  That, in turn, through use of the Pythagorean Theorem, is √(1^2+2^2), or √5.

Then cos x = adj side / hyp = 2/√5.  Rationalizing the denominator, we get

               2√5

cos x = -------------

                   5