You can begin by imagining a little triangle in the fourth quadrant to find your reference angle.  It would look like this:

Now, to find the sine of that angle, you will need to find the hypotenuse of the triangle. Using the Pythagorean Theorem, , where  and  are leg lengths and  is the length of the hypotenuse, the hypotenuse is , or, for our data:

The sine of an angle is:

For our data, this is:

Since this is in the fourth quadrant, it is negative, because sine is negative in that quadrant.

You can begin by imagining a little triangle in the third quadrant to find your reference angle. It would look like this: 

Now, to find the sine of that angle, you will need to find the hypotenuse of the triangle. Using the Pythagorean Theorem, , where  and  are leg lengths and  is the length of the hypotenuse, the hypotenuse is , or, for our data:

The sine of an angle is:

For our data, this is:

Since this is in the third quadrant, it is negative, because sine is negative in that quadrant.

Recall that the  triangle appears as follows in radians:

Now, the sine of  is . However, if you rationalize the denominator, you get:

Since , we know that  must be represent an angle in the third quadrant (where the sine function is negative). Adding its reference angle to , we get:

Therefore, we know that:

, meaning that 

Recall that the sine wave is symmetrical with respect to the origin. Therefore, for any value , the value for  is . Therefore, if  is , then for , it will be .

In a right triangle, for sides a and b, with c being the hypotenuse, . Thus if cos(A) is , then c = 14, and the side adjacent to A is 11. Therefore, the side opposite of angle A is the square root of , which is  Since sin is , sin(A) is .

As with all trigonometry problems, begin by considering how you could rearrange the question. They often have hidden easy ways out. So begin by noticing:

Now, you can treat  like it is any standard denominator. Therefore:

Combine your fractions and get:

Now, from our trig identities, we know that , so we can say:

Now, for our triangle, the  is . Therefore,

Recall that the standard  triangle, in radians, looks like:

Since , you can tell that .

Therefore, you can say that  must equal :

Solving for , you get:

sin(30º) = ½

sine = opposite / hypotenuse

½ = opposite / 8

Opposite = 8 * ½ = 4

Use SOHCAHTOA. Sin(30) = 12/x, then 12/sin(30) = x = 24.

You can also determine the side with a measure of 12 is the smallest side in a 30:60:90 triangle. The hypotenuse would be twice the length of the smallest leg.

We can solve for the length of the chord by drawing a line the bisects the angle and the chord, shown below as .

In this circle, we can see the triangle  has a hypotenuse equal to the radius of the circle (), an angle  equal to half the angle made by the chord, and a side  that is half the length of the chord.  By using the sine function, we can solve for .

The length of the entire chord is twice the length of , so the entire chord length is .