To solve this question, we need to use trigonometry, specifically the tangent of an angle in a right triangle. In this scenario, the building forms a right triangle with the ground and the line of sight from the point 25 meters away to the top of the building.
The tangent (tan) of the angle is defined as the ratio of the opposite side (the height of the building, which we are trying to find) to the adjacent side (the distance from the building, which is given as 25 meters). We can write this relationship as:
tan(angle) = opposite / adjacent
Given that the angle from the ground to the top of the building is 40°, we can denote this as:
tan(40°) = height of the building / 25
Using the tan function, we can solve for the height of the building:
height of the building = tan(40°) * 25
First, we calculate tan(40°). Without using a calculator, if you refer to trigonometry tables or a calculator, you would find that the tangent of 40 degrees is a constant value.
Next, we multiply this value by 25 to get the height of the building. This would give us the height in meters.
With this calculation, we discover that the height of the building is approximately 20.98 meters. Thus, the building is about 20.98 meters tall.
