Question

The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree whenseen from the top of the second tree is 45∘. If the height of the second tree is 80 m, find the height of the first tree.

Answer 1

The height of the first tree is 20 m. This is calculated by taking the height of the second tree (80 m) and subtracting the vertical distance (60 m) that corresponds to the horizontal distance between the two trees, based on a 45° angle of depression/elevation.

Step-by-step explanation:

To find the height of the first tree, we can use trigonometry. We know the angle of depression from the second tree to the first tree is 45°, the horizontal distance between the trees is 60 m, and the height of the second tree is 80 m. Since the angle of depression is equal to the angle of elevation when looking from the first tree to the second tree, we have a 45°-45°-90° right triangle.

Using the fact that the triangles in a 45°-45°-90° triangle are isosceles, we can say that the vertical distance from the first tree to the line of sight from the top of the second tree is also 60 m. Therefore, the height of the first tree is the height of the second tree minus this vertical distance, hence:

• Height of first tree = Height of second tree - Vertical distance
• Height of first tree = 80 m - 60 m
• Height of first tree = 20 m