The angle of elevation to the top of a very tall Building is found to be 9° from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the building.
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To find the height of the building, we can use basic trigonometry. Let's denote the height of the building as "h".
We have the following information:
- The angle of elevation to the top of the building is 9°.
- The distance from the base of the building is 1 mile.
We can use the tangent function to relate the angle of elevation to the height of the building.
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the building (h) and the adjacent side is the distance from the base of the building (1 mile).
tan(9°) = h/1
To find the value of tan(9°), we can use a calculator.
tan(9°) ≈ 0.15838
Now we can rearrange the equation to solve for h:
h = tan(9°) * 1
h ≈ 0.15838 * 1
h ≈ 0.15838
Therefore, the height of the building is approximately 0.15838 miles.
To find the height of the building, we can use the trigonometric relationship between the angle of elevation, the distance from the base of the building, and the height of the building.
Let's label the height of the building as "h" and the distance from the base of the building as "d".
We are given that the angle of elevation is 9° and the distance from the base of the building is 1 mile.
Using trigonometry, we can use the tangent function to relate the angle of elevation to the height and distance:
tan(angle of elevation) = height / distance
Plugging in the known values:
tan(9°) = h / 1 mi
Now, let's solve for h:
h = tan(9°) * 1 mi
To calculate this value, you can use a scientific calculator that has trigonometric functions or use an online calculator.
Using the formula, we find that h ≈ 0.1587 mi.
Therefore, the height of the building is approximately 0.1587 miles.