### Doug Riddle's "angle" on measuring big trees

Doug Riddle driddle@putzel.com

Here is my \$0.02 for measuring tree heights from another "angle". There are 2 trigonometric rules that govern what is done in measuring the height of trees. 1. For a triangle, if you know 2 angles and 1 length you can calculate the other angle and other 2 lengths. 2. For a triangle, if you know 2 lengths or "legs" of the triangle and the angle between the legs you can calculate the other length and other 2 angles. When you measure the height of a tree you are creating a "right" triangle. That is a triangle with one angle fixed at 90 degrees. So part of your work is done for you. Assuming a flat area of ground and a single visible crown: Using the clinometer and laser you can measure the angle to the highest crown of the tree and you can read the distance with the laser from you to that point at the crown of the tree. This gives you an angle and a length. The second angle is the 90 degree angle formed by an imaginary line from the tree's visible top to the horizontal ground. So you have the necessary information to know the height of the tree. The tree's height = laser distance x sine of the angle read with the clinometer.+ your height from eye level to ground. The sine of angles from 0 to 90 degrees is found either in a trigonometric table or by using a calculator with trig functions. You simply read the trig value of the angle and multiple times the laser distance.
Bob Leverett mentioned the fact that the clinometer gives you 2 numbers on the wheel insider the instrument. The number on the left, when you look inside the clinometer, is the angle value that you want to record. The number on the right is a percent value. The percent can be used to calculate the height of the tree based on another equation which I won't digress to explain. The value of using the laser is that you read the height from the point you see as the top of the tree to ground. This avoids the problem of measuring the angle to a high point on the tree and then pulling a tape from your reference point to the base of the tree and assuming that the high point is directly above the trunk of the tree. Whether the high point of the tree is over the trunk or not , the laser and clinometer gives you a true vertical distance for height.
The above example is the basic equation. There are endless variations. There are situations where you are not standing level with the base of the tree. Elementary trig equations can be used to solve these differences and give you an accurate height. Don't worry about the variations, just know that in time you will be able to handle all the variables.
Some priorities to keep in mind for now: A. Get far enough back to see the top of the tree. I try to be far enough back that the angle is less than 45 degrees. That is not a requirement, nor is it always possible; but if the angle is less than 45 degrees I seem to have a good view of the crown of the tree. B. Don't worry how far back you go, the laser will still give you a reading. The only time you will not get a laser reading is if you are less than the minimum distance. For the Bushnell 400 it requires a minimum distance of 25 yards. C. Walk around the tree looking for a window in the canopy to see clearly the top of the tree. The laser is sometimes fussy about having a clear view and you can get false short readings from intervening twigs and limbs. D. Use triangulation, (ie measure the height of the tree from more than one side), to find the highest point of the tree. A spreading crown obscures the top of many trees.
Some benefits: A. If you want a quick reading you can stand beneath the tree and use the laser for a vertical height. It will give you a "ball park" value to let you know if you want to take the time for a more accurate reading. Remember to add to your reading in this case your height from eye level to ground. B. If you are on one side of Cedar Cr. and the tree is on the opposite side you can still measure its height with the laser and clinometer. C. Similarly if the tree is a cypress in the middle of a body of water, you can use the laser for height and clinometer for angle and know the height above water of the tree. Of course you will not know that portion of the tree's height that is below water. D. If you are in a canoe you can still measure the height of the tree.