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 Question from Sarah, a student: I understand you do display questions very similar to this, but the slight differences between them are still causing me some confusion. Here is the question: 'A man standing 20metres away from a tower observes the angles of elevation to the top and bottom of a flag shaft standing on the tower as 62 degrees and 60 degrees respectively. Calculate the height of the flag shaft.' I have a rough idea how to draw the diagram, but it's the 'respectively' part I am unsure of, and whether to split it up into 2 (tower/flag shaft) or into 3 parts (tower/flag shaft/whole thing), before doing the calculations with Tan. Thankyou for your time.....

Sarah,

Respectively here means "in the same order". In the sentence "A man standing 20metres away from a tower observes the angles of elevation to the top and bottom of a flag shaft standing on the tower as 62 degrees and 60 degrees respectively." the top of the flag shaft is mentioned first so its angle of elevation is 62 degrees and the bottom of the flagpole is mentioned second so its angle of elevation is 60 degrees.

Look at the diagram in my response to Amber. You know the angles RSP and RSQ, and the distance x. Use the triangles RSP and RSQ to write the tangents of the two angles of elevation. One will give you the height of the tower and the other the tower plus the flag shaft.

I hope this kelps,
Penny

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