In parallelogram ABCD, the height dropped to side AB is 14, AD = 28. Find the sine of angle B.

Let the height from the top C – CH = 14 be lowered to the side AB; in triangle BCH, angle <BHC = 90 °, and BC is the hypotenuse of triangle BHC.

Then the sine of the angle B, sin B = HC / BC. But in the problem the value АD = 28 is known, but in the parallelogram АBСD of the side АD = ВС = 28, which means that

sin В = НС / ВС = 14/28 = 1/2, whence <В = arc sin (1/2) = 30 °.

Answer: <B = 30 °; sin B = 1/2.