。
She gave the elderly woman a warm smile.
Literal
She [topic-は] elderly-woman [at-に] warm smile [object-を] cast.
投げかける (なげかける) literally means 'to throw toward' but is commonly used figuratively for casting a smile, glance, or question at someone. 微笑 (びしょう, 'gentle smile') is a literary word. 老婦人 (ろうふじん) is a respectful term for an elderly woman — more polite than 老婆. The sentence has a narrative quality.