Question

The angle of elevation from the top of a 95 foot tall building to a hot air balloon in the sky is 76degree.If the horizontal distance between the building and the hot air balloon is 354feet, find the height of the air balloon.

Answer 1

Answer: $1,514.816\ feet$

Step-by-step explanation:

See the image attached, where "x" represents the height in feet of the hot air balloon.

Notice that:

$x=95+BC$

To find the lenght of the side BC of the right triangle, you need to use the following Trigonometric  Identity:

$tan\alpha=\frac{opposite}{adjacent}$

Observe that:

$\alpha =76\°\\opposite=BC\\adjacent=AC=354$

Substituting values and solving for "BC", you get:

$tan(76\°)=\frac{BC}{354}\\\\(tan(76\°))(354)=BC\\\\BC=1,419.816$

Therefore "x" is:

$x=95+1,419.816\\\\x=1,514.816$