Answer:
Approximately 213.294 feet
Step-by-step explanation:
To calculate the height of the leaning tower of Pisa, we can use trigonometry and the given information.
Let's denote the height of the tower as h.
From the given information, we have the following:
- The distance from the tower to the vertical line (the base) is given as 3.99° feet. Let's denote this distance as d.
- You are standing 200 feet from the tower.
- The angle of elevation from your position to the top of the tower is given as 44°46'.
We can set up a right triangle with the tower as the vertical side, the distance d as the horizontal side, and the height h as the hypotenuse.
Using trigonometric ratios, we can write the following equation:
tan(angle of elevation) = h / d
First, we need to convert the angle of elevation from degrees and minutes to decimal degrees:
44°46' = 44 + (46/60) = 44.767°
Now we can rearrange the equation to solve for h:
h = tan(angle of elevation) * d
Plugging in the values:
h = tan(44.767°) * 200
Using a calculator, we can find the value of tan(44.767°) ≈ 1.06647.
Therefore:
h ≈ 1.06647 * 200 ≈ 213.294 feet
The height of the leaning tower of Pisa is approximately 213.294 feet.
