SOLUTION: in a right triangle the sides a=2, and b=4, the function cos A equals?

To do that problem you must learn the parts of a right triangle. 
That is, you MUST learn:

1. What the leg opposite a given angle means
2. What the leg adjacent to a given angle means
3. What the hypotenuse means

The hypotenuse is the longest side of a right triangle. It is also
the side opposite the right angle.  "Opposite an angle" means
"across the triangle from the angle".

The other two sides of a right triangle are shorter than the
hypotenuse and are called "legs".

The leg which is next to an angle is called the "adjacent leg"
of that angle.

The leg which is NOT adjacent to but is across the triangle from
an angle is called the "opposite leg" of that angle.

Observe that the side which is opposite one acute angle is
adjacent to the other acute angle.

Then you MUST memorize the 3 trig ratios:

1. 

2. 

3. 

Those three are enough for calculating purposes, but there
are three other ones, the recip[rocals of the above: 

4. 

5. 

6. 

You must also memorize the standard labeling of a right triangle
ABC.

1. The right angle is labeled capital "C".

2. The leg opposite the angle A is labeled by the small letter "a".

3. The leg opposite the angle B is labeled by the small letter "B".

4. The hypotenuse is labeled by the small letter "c"

Now if you have memorized all that, then you are ready to
tackle this problem, but not until.

Your triangle is like this:

 

You ask yourself two questions:

1. What is given? 

2. What am I to find?

The answer to question 1 is "the leg a, opposite angle A, and leg b,
adjacent angle A"

The answer to question 2 is "the cosine of angle A"

Now you ask yourself this question:

Which of the first three trig ratios am I to find.

The answer is

2. 

That amounts to



You have b given but you don't have c.  So you calculate c by using

the Pythagorean theorem:















So now you can get 





Your teacher probably wants you to
rationalize the denominator and get



Edwin