SOLUTION
Let us use a simple diagram to interprete the question
In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.
So we will use the right-angled triangle formed to find h
As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA
[tex]\text{TOA tan }\theta=\frac{opposite}{\text{adjacent}}[/tex]So we have
[tex]\begin{gathered} \text{ tan }\theta=\frac{opposite}{\text{adjacent}} \\ \text{ tan }61.7\degree=\frac{h}{56.5} \\ 1.8572015=\frac{h}{56.5} \\ \text{cross multiplying, we have } \\ h=1.8572015\times56.5 \\ h=104.931887 \end{gathered}[/tex]Hence the answer is 104.9 feet to the nearest tenth
