Question

the angle of elevation from the top of a 95 foot tall building to a hot air balloon in the sky is 76 degrees . if the horizontal distance between the building in the hot air balloon is 354 ft, what is the height of the hot air balloon from the ground to the nearest tenth?

Answer 1

The situation described is shown in the following picture:

To find the height of the balloon from the ground we first need to find x. From the figure we notice that we have a right triangle and that we want the opposite leg of this triangle. If we remeber the definition of the tangent function:

`\tan \theta=\frac{\text{opp}}{\text{adj}}`

then we have in this case:

`\begin{gathered} \tan 76=(x)/(354) \\ x=354\tan 76 \\ x=1419.8 \end{gathered}`

Now we add the value of x to the height of the building:

`95+1419.8=1514.8`

Therefore the height of the balloon is 1514.8 ft