To find the height of the tree (\(h\)) in terms of the distance from the ranger to the tree (\(x\)), you can use the tangent function from trigonometry.
In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case:
- The height of the tree (\(h\)) is the length of the opposite side.
- The distance from the ranger to the base of the tree (\(x\)) is the length of the adjacent side.
- The angle between the ground and the line of sight to the top of the tree is 20°.
The tangent of the angle (20°) can be expressed as:
\[ \tan(20°) = \frac{h}{x} \]
To solve for the height of the tree (\(h\)), you can rearrange this equation:
\[ h = x \cdot \tan(20°) \]
Thus, the equation that can be used to find the height of the tree in terms of the distance from the ranger to the tree is:
\[ h = x \tan(20°) \]