First let's make a graph to understand the situation.
Now let's calculate the value for x, using the trigonometric relation of the tangent.
[tex]\begin{gathered} \tan 56=x/150 \\ x=150\cdot\tan 56 \\ x=222.38\text{ ft} \end{gathered}[/tex]
In a similar way we will calculate the value of y
[tex]\begin{gathered} \tan 32=y/150 \\ y=150\cdot\tan 32 \\ y=93.73 \end{gathered}[/tex]
The total height of the building would be the sum of the x and y values.
[tex]\begin{gathered} d=x+y \\ d=316.1\text{ ft} \end{gathered}[/tex]
To the nearest tenth of a foot, the building is 316.1 feet tall.
