Using Tangent to the calculate the height of a tree.
To find the height of the tree without climbing it you would need a 10-foot or so measuring tape, a 180 degree half-circle compass, eyes, and a Tangent Trigonometry table (based measurements generated by the Pythagorean Theorem A^2+B^2=C^2 for right triangles). From SOHCAHTOA we know that Tangent (of the angle) = Opposite / Adjacent, so we imagine a big right triangle where the Opposite side is from the top of the tree to where the tree meets the ground and the Adjacent side is measured with the measuring tape as being the distance from the base of the tree to the center of the compass where you are at with the compass on the ground. The angle from the center of the compass on the ground to the top of the tree is at is the Tangent angle. So the height of the tree (the Opposite side) is the Adjacent side length times the Tangent of the angle. This method can also be used to find the distance across a river without crossing it. If you did not have eyes you physically measure the distance from the compass to the base of the tree (or use an ultrasonic proximity detector (a rangefinder)), and you could point a laser from the compass to the top of the tree and the angle at which a the laser dot is visible on the top of the tree is the angle to apply to the Tangent function. Another way is to use a yellow laser and a blue laser to produce a green dot, or one laser and a rainbow prism for the angle at which the colors mix correctly. 
Justin Coslor 4/10/2020