First, let's draw a scheme representing the measures in the text. Let's call the shorter building as A and the taller building as B.
Using this scheme, we can see that we have 2 right triangles. The height of the taller building(let's call it hB), is given by the following relation
[tex]\frac{h_B_{}}{67}=\tan 39^o[/tex]Then, calculating the height we have
[tex]\begin{gathered} h_B=67\tan 39^o=67\times0.80978403319\ldots=54.2555302241 \\ h_B\approx54.3 \end{gathered}[/tex]The difference between the height of the smaller building(let's call it hA) and the taller building, is given by
[tex]\frac{(h_B-h_A)}{67}=\tan 27^o[/tex]Solving for h_A, we have
[tex]\begin{gathered} \frac{(h_B-h_A)}{67}=\tan 27^o \\ (h_B-h_A)=67\tan 27^o \\ h_A=h_B-67\tan 27^o \\ h_A\approx20.1 \end{gathered}[/tex]The height of the smaller building is 20.1m and the height of the taller building is 54.3m.
