To a man standing outside his house, the angles of elevation of the top and bottom of a window are \(60^{\circ}\) and \(45^{\circ}\) respectively. If the height of the man is \(177 \ cm\) and if he is \(3 \ m\) away from the wall, what is the height of the window? (\(\sqrt{3} = 1.732\))
Answer:
Let \(AB\) be the height of the man. Let \(C\) and \(D\) be the top and bottom of the window. Let \(BE\) and \(AF\) be the distance between the man and the wall.
In the right \(\triangle AFD\), \(tan \ 45^{\circ} = \frac{DF}{AF}\)
\(\Rightarrow\)
In the right \(\triangle AFC\), \(tan \ 60^{\circ} = \frac{CF}{AF}\)
\(\Rightarrow\)
Solving the above two equations, we have:
The height of the window \(=\) .
(Note: Enter the number rounded off to two decimal places in the first box and the unit (short form) in the second box.)