To determine the angle of elevation from the boy's eye to the top of the tower, we can use trigonometry, specifically the tangent function.
First, let's draw a diagram to understand the situation. The tower can be represented as a vertical line, and the boy can be represented as a point on the ground. The line connecting the boy's eye to the top of the tower would form a right triangle with the ground.
Now, we have the following information:
- The height of the tower = 30m
- The distance between the boy and the tower = 20m
- The boy's height = 1.5m
To find the angle of elevation, we need to find the ratio between the opposite side (tower height) and the adjacent side (distance between the boy and the tower). This ratio is defined as the tangent of the angle of elevation.
So, we can calculate the tangent of the angle as:
tan(angle) = opposite/adjacent
tan(angle) = height of the tower/distance between the boy and the tower
tan(angle) = 30m/20m
tan(angle) = 3/2
Now, to find the angle itself, we can take the inverse tangent (also called arctan or tan^-1) of both sides, which will give us the angle itself instead of the ratio:
angle = arctan(3/2) ≈ 56.31 degrees
Hence, the angle of elevation from the boy's eye to the top of the tower is approximately 56.31 degrees.