Answer: [tex]1,514.816\ feet[/tex]
Step-by-step explanation:
See the image attached, where "x" represents the height in feet of the hot air balloon.
Notice that:
[tex]x=95+BC[/tex]
To find the lenght of the side BC of the right triangle, you need to use the following Trigonometric Identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
Observe that:
[tex]\alpha =76\°\\opposite=BC\\adjacent=AC=354[/tex]
Substituting values and solving for "BC", you get:
[tex]tan(76\°)=\frac{BC}{354}\\\\(tan(76\°))(354)=BC\\\\BC=1,419.816[/tex]
Therefore "x" is:
[tex]x=95+1,419.816\\\\x=1,514.816[/tex]
