We will have the following:
In order to determine the height of the building we will rememer that:
[tex]\sin\lparen\theta)=\frac{opposite}{Hypotenuse}[/tex]So:
[tex]\sin\mleft(51\mright)=\frac{h}{100}\Rightarrow h=100\sin\lparen51)[/tex][tex]\Rightarrow h=77.71459615...\Rightarrow h\approx77.7[/tex]So, the height of the building is approximately 77.7 feet.