We can calculate the height of Tree mathematically if we have information about distance of tree from itself and angle of elevation. If we have these two factors then we can measure height of tree. Let us see how to find height of tree if elevation and distance is given.
Step 1: First we need to draw a triangle. This triangle must have a Right Angle and two acute angles. This triangle is formed by three sides. Hypotenuse is just opposite to angle of 90 degree.
Step 2: Now we will walk some defined distance from the tree. So this distance is known value to us. We know that how far away we are from tree. The angle between ground and tree is a right angle which is of 90 degrees. The distance is also an adjacent side of right angle.
In this triangle hypotenuse is the side or leg which is the distance from a person to top of the tree.
Step 3: Now we know that angle of elevation so it will be not be difficult to calculate the height of tree
Step 4: Elevation angle is the Ratio of ground distance and hypotenuse. We do not know the hypotenuse but we can measure it by cosine function.
Step 5: Sin function of angle is the ratio of height and hypotenuse. We have both values sin angle and hypotenuse. So now we can calculate the opposite side that is the height of tree. When we multiply the hypotenuse by value of sin angle of elevation then we will get height of the tree.