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.
1 mile = 5280 feet
h/5280 = tan 9°
h = 5280 * .15838
h = 836.24
To find the height of the building, we can use trigonometry, specifically tangent (tan) function.
Let's label the height of the building as 'h'. We are given that the angle of elevation to the top of the building is 9°.
Now, we can create a right triangle with the base being the distance from the building (1 mi) and the height (h) being the length from the top of the building to the observer on the ground. The angle between the base and the height is 90°, and the angle between the base and the line of sight to the top of the building is 9°.
Using the tangent function:
tan(angle) = opposite/adjacent
In this case, tan(9°) = h/1.
To solve for h, we can multiply both sides of the equation by 1:
1 * tan(9°) = h.
Using a calculator, we find that tan(9°) is approximately 0.1584.
Therefore, the calculation becomes:
h = 1 * 0.1584.
The height of the building is approximately 0.1584 mi.
Note: Make sure to convert units if needed. In this case, since the distance is given in miles, the height of the building will also be in miles.