The top of a building 24 meter high is observed from the top and from the bottom of the vertical tree. The angle of elevation are found to be 45 degree and 60 degree respectively. Find the height of the tree

Answer 1

Let's assume the height of the tree is h meters.
From the top of the building, the angle of elevation is 45 degrees, meaning the observer's line of sight forms a 45-degree angle with the horizontal. This forms a right triangle with the building height as the opposite side and the distance from the tree to the building as the adjacent side.
Using the trigonometric ratio for tangent, we have:
tan(45°) = building height / distance from the tree to the building
1 = 24 / distance from the tree to the building
distance from the tree to the building = 24 meters

From the bottom of the tree, the angle of elevation is 60 degrees, meaning the observer's line of sight forms a 60-degree angle with the horizontal. This forms a right triangle with the height of the tree as the opposite side and the distance from the tree to the building as the adjacent side.
Using the trigonometric ratio for tangent, we have:
tan(60°) = height of the tree / distance from the tree to the building
√3 = h / 24
h = 24√3 meters

Therefore, the height of the tree is approximately 41.57 meters.