Answer:
The height of the tree is 19.81 m
Step-by-step explanation:
Trigonometric Ratios
The ratios between the sides of a right triangle are called trigonometric ratios.
If any of the acute angles is chosen as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides and the hypotenuse.
The image shows a right triangle with a tree and the ground forming a right angle and an elevation angle of 33°.
This angle of 33° has a side of 30.5 m as its adjacent leg and the height of the tree X as the opposite side.
The trigonometric ratio that relates both legs is the tangent:
[tex]\displaystyle \tan 33^\circ=\frac{X}{30.5}[/tex]
Solving for X
[tex]X=30.5\cdot \tan 33^\circ[/tex]
Using a calculator:
X = 19.81 m
The height of the tree is 19.81 m
