The method Using a Clinometer or Transit goes into the full calculations and reasons why this work, but you don’t need to go into it to find the height using this method.
The triangle will have one right (90 degree) angle and two 45 degree angles.
The longest side, the one you’ll be looking along, is called the hypotenuse of the triangle.
To learn how this works, see the “Using a Clinometer or Transit” section. You don’t need to do any calculations in this method, because there’s a little trick: the tangent of a 45º angle (which you used) equals 1. The equation can be simplified to this: (Height of tree) / (distance from tree) = 1. Multiple each side by (distance from tree) and you get: Height of tree = distance from tree.
If you want to avoid doing any math at all, you can use a tree height calculator online, such as this one, and enter the measurements you find using this method.
You’ll need a single number, such as your height in inches, not a combination of feet and inches. If you’re not sure how to convert into one number, you can use the height of a yardstick or meter ruler standing vertical instead (3 feet or 1 meter). Use the ruler’s height and the length of the ruler’s shadow anytime you are asked to use If you are in a wheelchair or cannot stand straight for another reason, measure your height in whatever position you’ll be in when you go outside to measure the tree.
Write down and label each measurement you make right after you make it, to avoid confusing them with each other.
If the tree’s shadow is on a slope, there might be a different time of day when the shadow avoids the slope either by being shorter or by pointing in the other direction.
Measure the width of the trunk with a long ruler or straight tape measure, then divide by 2 to get 1/2 the tree’s width. If you’re having trouble seeing how wide the trunk is, draw a tight square around the base of the trunk and measure one side of that square.
Multiply the length of the tree’s shadow by your height. If you are 5 feet (1. 5 meters) tall, and the tree’s shadow is 100 feet (30. 48 meters) long, multiple them together: 5 x 100 = 500 (or for the meter measurements, 1. 5 x 30. 48 = 45. 72). Divide the answer by the length of your shadow. Using the example above, if your shadow is 8 feet (2. 4 meters) long, divide your answer by that number. 500 / 8 = 62. 5 feet (or in metric, 45. 72 / 2. 4 = 19. 05 meters). If you’re having trouble with the math, find a tree height calculator online such as this one.
Note: If you do have a tape measure with you when you’re near the tree, you do not need to do any calculations. Read the step above for “if you have a tape measure” carefully.
The Piece of Paper method actually uses a piece of paper as a clinometer. This method, besides being more accurate, allows you to measure the height from any distance, instead of moving forward and backward to get the paper to line up with the tree.
Click this link to go to an online tangent calculator. The tangent of an angle in a right triangle is defined by the side opposite the angle, divided by the side adjacent to the angle. In this case, the opposite side is the height of the tree, and the adjacent side is your distance from the tree.
If you read the earlier substep about the definition of the tangent, you can see why this method works. As described earlier, the tangent = (tree’s height) / (distance to tree). Multiply each side of the equation by the (distance to tree) and you get (tangent) x (distance to tree) = (the tree’s height)!
If you are using a stationary transit, add the height from the transit eyepiece to the ground, not your own height.
