EXPLANATION
Let's represent the situation on a graph:
Let's call x to the height of the tower.
The height of the tower is given by the following trigonometric relationship:
[tex]\text{tangent 40}=\frac{opposite\text{ cathetus}}{\text{adjacent cathetus}}[/tex]Replacing terms:
[tex]\text{tangent 40 = }\frac{x}{120}[/tex]Multiplying 120 to both sides:
[tex]120\cdot tangent\text{ 40 = x}[/tex]Solving the argument:
[tex]120\cdot0.72=\text{ x}[/tex]Multiplying numbers:
[tex]120\cdot0.72=86.4\text{ ft}[/tex]The tower is 86.4 ft tall
