Dr. and Mrs. Ballard Hayworth of Woodside, Cal. have announced the engagement of their daughter, Nancy Hayworth Whiteley, to Ralph E. Becker, Jr. of Salt Lake City, Utah. He is the son of former Ambassador and Mrs. Becker of Washington, D.C.

The future bride attended the School of Nursing at the University of Utah and is currently an ophthalmic technician with an ophthalmologist in San Carlos, Cal. The future bridegroom graduated from St. Albans School here, attended Lafayette College and graduated cum laude from the University of Pennsylvania. Mr. Becker received the JD from the University of Utah Law School, is a candidate for an MS in geology with an emphasis in regional environmental planning and is associated with Bonneville Associates, a consulting firm in Salt Lake City as Counsel, Government Relations.

Dr. Hayworth is a partner in the Redwood Medical Clinic, Redwood City, Cal., and associated with the School of Medicine at Stanford University. Mr. Becker's father is counsel to the Washington law firm of Landfield, Becker and Green, and is president of the Voice Foundation. A former Chairman of the Young Republican National Federation, he was appointed by President Eisenhower in 1958 as General Counsel and a Founding Trustee of what was then the National Cultural Center and now the John F. Kennedy Center for the Performing Arts, and in 1976 President Ford appointed him United States Ambassador to Honduras.

The prospective bride's grandparents are Mrs. Harvey P. Baird of Cedar Falls, Iowa, and the late Mr. Baird and of Mrs. D.A. Hayworth of Sioux City and Menlo Park, Cal., and the late Mr. Hayworth -- the distinguished educator.Mr. Becker is the grandson of Mrs. William G. Watters of New York City and Washington, D.C., and the late Mr. Watters, who was founder in 1906 with is brother, the noted scientist Dr. Leon L. Watters, of the Watters Laboratories and the Hospital Supply Company in New York. His ancestors were early pioneers of Utah and California and he is the grandson of the late Mr. and Mrs. Max J. Becker of Port Chester, N.Y.

After their marriage on June 28 in Woodside, the couple will live in Salt Lake City.