First lets sketch the situation:
The position of the bird with the vertical height and the distance to the observer form a right triangle.
We know the angle of elevation from the person's stand point and the distance between the person and the school represents the adjacent side to the angle and the base of the right triangle. The heigh the bord flies is the height of the triangle and opposite side to the angle of elevation.
To determine the length of the opposite side you have to use the trigonometric ratio that relates the adjacent and opposite sides of the triangle. That is the tangent:
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]θ is the angle of elevation
The adjacent side measures 500m
The opposite side measures x
[tex]\begin{gathered} \tan 39=\frac{x}{500} \\ x=\tan 39\cdot500 \\ x=\sqrt[]{3} \\ x\cong1.73m \end{gathered}[/tex]The bird flies at 1.73m from the groud.
