SOLUTION: in a right triangle with the hypotenuse c=10 and the angle A=50 degrees the side b 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 hypotenuse c and the angle A"

The answer to question 2 is "the side b which is opposite angle B, and
adjacent to angle A"

Now you ask yourself this question:

Which of the first three trig ratios involves
only what is given and what I am to find.

You look through these:

1. 

2. 

3. 

and you observe that only one of these three involves both
what you are given and what you are to find and that is

2. 

So you substitute A = 50° and b for the leg adjacent angle A,
and 10 for c, the hypotenuse:



Now put a 1 under the term on the left:



And cross-multiply, getting



Now get you calculator, make sure it's in degree mode,
not radian mode, and punch the answer out as



If your teacher says to round it off to a certain number of
decimal places according to some rule, then follow the rule
and round it to, say, 

Edwin