How to measure the height of a tree using trigonometry?
We can make use of the tangent function in trigonometry to find the height of the triangle.
Answer: Basic trigonometric formulas for tangent functions can easily help us to find the height of the tree.
Go through the explanation to understand better.
Explanation:
Material required for the measurement:
1) A measuring tape, 2) A calculator with cosine and tangent functions, 3) An inclinometer to measure the angles.
Measurement of Height of the Tree: Measuring the height of a large tree can prove to be a tedious task, but trigonometry makes it way easier than we could have ever imagined it to be. The measurement becomes more reliable, as we move farther from the tree. Depending upon the slope of the ground on which the observer and the tree are located, various formulas can be devised for finding the height of the tree, and are given one by one, below:
Working on level ground: Measurement of height of tree requires basic trigonometric formula, that is, h = Tan A × d, where h = height of the tree, d = distance of the observer from the tree, A = angle to the top of the tree.
Working on slightly sloped terrain: We need to measure additional angles when the gradient is such that the base of the tree is slightly above or below the eyesight. Thus, the additional angles measured are \((A)_{1}\) = top of the base of the tree and \((A)_{2}\) = bottom of the tree
