The situation described is shown in the following picture:
To find the height of the balloon from the ground we first need to find x. From the figure we notice that we have a right triangle and that we want the opposite leg of this triangle. If we remeber the definition of the tangent function:
[tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]then we have in this case:
[tex]\begin{gathered} \tan 76=\frac{x}{354} \\ x=354\tan 76 \\ x=1419.8 \end{gathered}[/tex]Now we add the value of x to the height of the building:
[tex]95+1419.8=1514.8[/tex]Therefore the height of the balloon is 1514.8 ft
