Help sketch and solve this!
From an eye level that is 6 ft above ground, the angle of elevation of the top of a building is 84 degrees and the angle of depression of the base of the building is 19 degrees. Approximate height of building.

Question

Help sketch and solve this!
From an eye level that is 6 ft above ground, the angle of elevation of the top of a building is 84 degrees and the angle of depression of the base of the building is 19 degrees. Approximate height of building.

babynini · Answer

Is this correct?

babynini · Answer

(In Red = all the information they gave me. I drew the picture from the info and calculated the other answers.)

babynini · Answer

@asnaseer, @Astrophysics ? :)

asnaseer · Answer

Yup - it all looks correct to me. The only advice I would give you is to try and leave the actual calculations in questions like this to the very end.

So you got:$$x=\frac{6}{\tan(19)}$$Then you got:$$y=\tan(84)\times\frac{6}{\tan(19)}=\frac{6\tan(84)}{\tan(19)}$$and finally:$$h=y+6=\frac{6\tan(84)}{\tan(19)}+6$$Once you get to this, then do the calculations. Tat way you will have less rounding errors along the way.

babynini · Answer

Okay! Yeah I put the numbers calculated into my calculator storage so that I wouldn't be rounding. But the way you did it is even more simple and accurate. Thanks, I hadn't thought of doing that :)

asnaseer · Answer

yw :)

Also, if you do it this way then sometimes a lot of the terms just cancel out, leaving you with a much simpler calculation at the end.

babynini · Answer

ooo that's fantastic haha.

asnaseer · Answer

:)

babynini · Answer

Oh, actually, quick question. The prof asks me to "consider checking the correctness of the solution in the original problem statement, it should make sense."
Is there anyway to do that in this problem?
It may give me more points if I do that but idk how :P