To throw something toward someone, or to direct a look/light/question at someone; figuratively, to pose or raise an issue.
子供が友達にボールを投げかけた。
The child threw a ball to his friend.
彼女は彼に優しい微笑みを投げかけた。
She cast a gentle smile at him.
その映画は観客に多くの疑問を投げかける作品だ。
That film is a work that raises many questions for the audience.
演説でリーダーは市民に課題を投げかけた。
In his speech the leader posed challenges to the citizens.