You are standing 46 meters from the base of a building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82°. If the total height of the building is another 121 meters above the 86th floor, what is the approximate height of the building?
height = base* tan(82)
46 * 7.11536 = 327.31
327.32 + 121 = 448.31 meters
Correction: 327.31 + 121 = 448.31 meter*
To find the approximate height of the building, we can use trigonometry.
First, let's create a right triangle using the given information.
The base of the right triangle is the distance from where you are standing to the base of the building, which is 46 meters. The height of the right triangle represents the height of the building from the base to the top of the 86th floor, which is what we are trying to find.
Using the angle of elevation, which is 82°, we know that the angle opposite the base of the right triangle (the angle between the base and the line of sight to the top of the 86th floor) is also 82°.
Now, using the tangent function, we can find the height of the building from the base to the top of the 86th floor:
tan(82°) = height of the building / 46 meters
Now, we can solve this equation for the height of the building:
height of the building = tan(82°) * 46 meters
Calculating this using a calculator:
height of the building ≈ 120.68 meters
So, the approximate height of the building, including the additional 121 meters above the 86th floor, is approximately:
Total height of the building = height of the building + 121 meters
Total height of the building ≈ 120.68 meters + 121 meters
Total height of the building ≈ 241.68 meters
Therefore, the approximate height of the building is approximately 241.68 meters.
To find the approximate height of the building, we can use the concept of trigonometry and the given information about the angle of elevation.
1. Let's draw a diagram to understand the situation better. Draw a right-angled triangle with one side representing the distance from your position to the base of the building (46 meters), the other side representing the height of the building (x meters), and the hypotenuse representing the line of sight from your position to the top of the building.
```
|\
| \
x | \ 121
| \
| \ \
|______\
46 meters
```
2. Since we are given the angle of elevation, we can use the tangent function (tan) to relate the angle of elevation to the sides of the triangle:
tan(angle of elevation) = opposite / adjacent
In this case, the opposite side is the height of the building (x) and the adjacent side is the distance from your position to the base of the building (46 meters).
So, we have: tan(82°) = x / 46
3. To solve for x, we can rearrange the equation:
x = 46 * tan(82°)
4. Now, we can calculate the value of x using a scientific calculator or computer:
x ≈ 46 * tan(82°) ≈ 205.366 meters
5. However, we need to find the total height of the building, including the 121 meters above the 86th floor. Therefore, the approximate height of the building is:
Total height = x + 121 = 205.366 + 121 = 326.366 meters
So, the approximate height of the building is around 326.366 meters.