The height of the air balloon can be calculate by using trigonometric Identities formula.
The height of the hot air balloon is 1514.82 feet.
Given:
Angle of elevation is [tex]\ 76 ^{\circ}[/tex].
Building height is [tex]95\:\rm foot[/tex].
The distance between building and hot air balloon is [tex]354 \:\rm feet[/tex]
Draw the figure according to given question.
Write the trigonometric identity tangent function to find the height.
[tex]\tan\theta = \dfrac {\rm Opposite} {\rm Adjacent}[/tex]
Substitute the value.
[tex]\begin{aligned}\tan76^{\circ} &= \dfrac {h} {354}\\h&=354\times \tan76^{\circ}\\h&=1419.81645\end {aligned}[/tex]
The total height of the balloon from the ground is the height of the building.
[tex]\{\rm Total\: height}=1419.81645 + 95 = 1514.81645 \:\rm feet[/tex]
Thus, the height of the hot air balloon is 1514.82 feet.
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