The angle of elevation to the top of a very tall Building is found to be 15° 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 trigonometry. Let's label the height of the building as "h" and the distance from the base of the building to the point where the angle of elevation is measured as "x".

From the given information, we know that the angle of elevation is 15°, and the distance from the base of the building to the measuring point is 1 mile (x = 1 mile).

Now, we can use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle. 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 (x).

The tangent of the angle of elevation is given by the formula:

tan(angle) = opposite/adjacent

In our case, tan(15°) = h / 1 mile.

To find the height of the building (h), we can rearrange the equation:

h = tan(angle) * x

Plugging in the given values, we have:

h = tan(15°) * 1 mile

Now, we can use a calculator to find the tangent of 15°:

tan(15°) ≈ 0.26794

Therefore, the height of the building is:

h ≈ 0.26794 * 1 mile ≈ 0.26794 miles.

So, the height of the building is approximately 0.26794 miles.