Find the side CD of triangle BCD if you know BC = 4, BD = 8, cosB = 11/16.

Given:
triangle BCD,
BC = 4,
BD = 8,
cosB = 11/16.
Find the length of the side of a triangle CD -?
Decision:
Consider a triangle BCD. By the cosine theorem (the square of a side is equal to the sum of the squares of the other two sides without doubled the product of these sides by the angle between them):
CD ^ 2 = BC ^ 2 + BD ^ 2 – 2 * BC * BD * cosB;
CD ^ 2 = 4 ^ 2 + 8 ^ 2 – 2 * 4 * 8 * 11/16;
CD ^ 2 = 16 + 64 – 8 * 8 * 11/16;
CD ^ 2 = 16 + 64 – 64 * 11/16;
CD ^ 2 = 80 – (64 * 11) / 16;
CD ^ 2 = 80 – (4 * 11) / 1;
CD ^ 2 = 80 – 44;
CD ^ 2 = 36;
CD = 4.
Answer: 4