MATHSMATHSAMATHS , welcome to MHF.
If d is the distance between K and C, hen KC = h, because angle of elevation to G is 45 degrees.
Distance between B and K is
So tan(30) =
hey, ive been working on this question for a while now; i just cant seem to get it.
A building is in the shape of a square prism with base edge m and height h metres. It stands on level ground. A base diagonal AC is extended to point K.
From K, a surveyor finds that the angles of elevation of F and G are 30 degrees and 45 degrees respectively. Find an exact value for the ratio h/m.
The top square base is read with vertices (left to right to bottom right to bottom left) H, G, F, E.
the bottom square is read with vertices ( left to right to bottom right to bottom left) D, C, B, A.
Edit: I guess it's unambiguous after all, but still requires too much inferring from context for my taste. sa-ri-ga-ma's post will lead you to the answer.
The problem is really complicated. The observer sees the perspective view of the prism.
Since the height of the observer is not given, we have to assume that the eye sight is along the ground level. So the observer sees BCD in the same level.
When the observer moves from the center of face BC to the line along BC, side m shrinks from m to zero. When he is along AC, m' = mcos(45)
Because of the perspective view, h also shrinks. Since angle of elevation of G is 45 degrees and that of F is 30 degrees, h' = h - m'tan(15) and KC = h
The apparent distance KB =
Now tan(30) =
After simplification and squaring , you get
Substituting the value of m' and dividing h^2 on both side, solve the quadratic to find m/h.