Question

An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is ${45}^{\circ }$. The height of the chimney is?

Answer 1

The given situation can be represented by the figure below:

$tan\left(\angle C{A}^{{}^{\prime }}{B}^{{}^{\prime }}\right)=\frac{C{B}^{{}^{\prime }}}{A^{{}^{\prime }}{B}^{{}^{\prime }}}\Rightarrow tan{45}^{\circ }=\frac{C{B}^{{}^{\prime }}}{28.5m}\Rightarrow 28.5\times 1=C{B}^{{}^{\prime }}Heightofchimney=C{B}^{\prime }+B{B}^{\prime }=28.5+1.5=30m$