Look at the attached figure. We define the unit circle as a circle with center in the origin (0,0) and radius 1.
Then, we consider a point P on the circumference. We call the angle between the positive half of the x axis and the radius AP.
We define
As you can see, ACD is a right triangle, and so we have
But since we know that AD is the cosine, AC is the sine, and AP is the radius (which is 1, and remains 1 when squared), we have just found out that
Answer:
12.87
Step-by-step explanation:
Since we know that line CD is a perpendicular bisector, triangle ACD is a right triangle, and thus we can apply the Pythagorean theorem to determine the length of side CD. Since the Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the adjacent sides, we can plug in the values of side AD and AC.
As side CD is the bisector of side AB, sides AD and DB are both half the length of side AB, so:
AD = 11/2
AD = 5.5
We now know two values of our equation, and thus we can solve for the missing third value.
5.5^2 + b^2 = 14^2
14^2 - 5.5^2 = b^2
196 - 30.25 = b^2
165.75 = b^2
b = 12.87