Heights And Distances

Let the height of the tree be and the length of the shadow of the tree be . According to the problem, the length of the shadow is times the height of the tree: $ be the angle of elevation of the Sun. We can consider a right-angled triangle formed by the tree (perpendicular), its shadow (base), and the line from the top of the tree to the end of the shadow (hypotenuse). The angle of elevation is the angle between the ground (shadow) and the line of sight to the top of the tree. We can use the tangent function, which relates the angle to the opposite side (height of the tree) and the adjacent side (length of the shadow): \) and : \) whose tangent is . We know from trigonometric values that: \) $ Therefore, the angle of elevation of the Sun is .

Let the height of the tree be and the length of the shadow of the tree be . According to the problem, the length of the shadow is times the height of the tree: $ be the angle of elevation of the Sun. We can consider a right-angled triangle formed by the tree (perpendicular), its shadow (base), and the line from the top of the tree to the end of the shadow (hypotenuse). The angle of elevation is the angle between the ground (shadow) and the line of sight to the top of the tree. We can use the tangent function: \) and : \) whose tangent is . We know from trigonometric values that: \) $ Therefore, the angle of elevation of the Sun is .