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 balloo…

Question

asked Dec 24, 2020 94.5k views

1 Answer

Nicolas Bonnet · Answer 1 · 2020-12-30T05:02:00+0000

Answer:
$1,514.816\ feet$

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:

$tan\alpha=(opposite)/(adjacent)$

Observe that:

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

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

$tan(76\°)=(BC)/(354)\\\\(tan(76\°))(354)=BC\\\\BC=1,419.816$

Therefore "x" is:

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