The give situation can be illustrated as follow:
As you can notice, the vertical distance between the balloon and the ground, the distance between the balloon and the headquartes and distance between vertical line and headquarter form a right triangle.
In order to determine the distance from the headquarter to a point on the ground just below the ballon, use the tanx:
[tex]tanx=\frac{opposite}{adjacent}[/tex]Here, opposite is the required distance and adjacent is 777ft. x is a complementary angle to 78.4, then, you have:
x + 78.4 = 90
x = 90 - 78.4
x = 11.6
Solve for oppopsite in the equation for tanx, replace the values of the other parameters and simplify:
[tex]\begin{gathered} opposite=adjacent*tanx \\ opposite=(777ft)tan11.6 \\ opposite\approx159.5ft \end{gathered}[/tex]Hence, the distance from the headquarter to a point on the grpund directly below the balloon is approximately 159.5ft
