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Exam-Style Question on Trigonometry

A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 460. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

Melissa has a webcam on the top of her computer screen. She has the zoom level adjusted so that that her head is framed nicely in the image produced. The diagram shows the setup.

Webcam range

The webcam is at point C directly above point D on the floor. The area covered by the camera is shown by the shaded region enclosed by triangle ABC. The distance from A to C is 4 m and the distance from A to B is 1.3 m. Angle ACB is 16o.

(a) Find angle ABC.

Melissa's younger brother is 95cm tall. He walks into the room from the door at the opposite end of the room from Melissa's computer. When he reaches point A his feet first appear in the video being recorded by the webcam. He continues to walk until the top of his head is in shot at which points he stops.

(b) How far is Melissa's brother from point A?

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