using the trigonometric ratio
[tex]\begin{gathered} \tan 30^{\circ}=\frac{opposite}{\text{adjacent}} \\ \end{gathered}[/tex][tex]\begin{gathered} \tan 30^{\circ}=\frac{h}{8} \\ h=8\tan 30^{\circ} \\ h=8\times0.57735026919 \\ h=4.61880215352 \\ h\approx4.62m \end{gathered}[/tex]My choice of the trigonometric function above is base on the fact that we want to the find opposite side(height of tree) of the triangle and the adjacent side was also given. It's only logical to use the tangential ratio which requires the opposite side(unknown side, h) and the adjacent side(given side, 8 m). Using this, we can find the required missing side(h).
The reason why the other trigonometric function (sin and cos) won't work is that we were not given the hypotenuse of the right-angle triangle. Since we are asked to find the height of the tree(h) which is the opposite side of the triangle, the other side given was the adjacent side(8 m) of the triangle. Assuming the other side given is the hypotenuse, sin function (sin 30 = opposite/hypotenuse) can be used to find the height of the tree. Generally. the sin and cos ratio requires the hypotenuse sides.
Note the side opposite the angle used is the opposite side of the right-angle triangle.