Answer:
F. 34.64 m
Step-by-step explanation:
The measurements given in the question are;
The angle (of depression) given by the clinometer, θ = 30°
The horizontal distance of the lunchbox from the tree, d = 20 meters
The height (how tall) of the tree = Required
Let the height of the tree be assumed to be perpendicular to the ground, noting that the horizontal distance from the lunchbox to the tree is a straight line, let <em>l</em> represent the line of sight from the top of the tree to the lunchbox, and let <em>h </em>represent the height of the tree we have;
The line of sight to the lunchbox, <em>l</em>, the height of the tree, <em>h</em>, and the horizontal distance of the lunchbox from the base of the tree form a right triangle
The height of the tree is the adjacent leg to the given angle by the clinometer
Using trigonometric ratios, we have;
tan(30°) = d/h
∴ tan(30°) = (20 m)/h
h = (20 m)/tan(30°) ≈ 34.64m
The height of the tree, h ≈ 36.64 m.
