The angle of elevation to the top of a Building in New York is found to be 6 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.
the height in feet can be found using
h/5280 = tan6°
To find the height of the building, we can use the tangent function, which relates the angle of elevation, the height, and the horizontal distance between the observer and the base of the building.
We are given that the angle of elevation is 6 degrees and the distance from the base of the building is 1 mile. Let's first convert the distance to feet, since the height will be in the same unit.
1 mile is equal to 5280 feet.
Now, let's consider a right triangle with the observer at one end, the top of the building at the other end, and the base of the building forming the adjacent side to the angle of elevation of 6 degrees.
By definition, tangent θ is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the building and the adjacent side is the distance of 5280 feet.
Using the tangent function: tan(6 degrees) = height / 5280 feet.
To find the height, we can rearrange the equation: height = tan(6 degrees) * 5280 feet.
Now, let's calculate the height:
height = tan(6 degrees) * 5280 feet
≈ 0.1051 * 5280
≈ 554.88 feet.
Therefore, the height of the building in New York is approximately 554.88 feet.
To find the height of the building, we can use the trigonometric relationship between the angle of elevation and the height of the building.
Let's assume that the height of the building is represented by 'h'.
We have the following information:
- Angle of elevation = 6 degrees
- Distance from the base of the building to the point of observation = 1 mile
Now, we can use the tangent function to find the height of the building.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. 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 to the observer (1 mile).
Using trigonometry, we can set up the equation:
tan(6 degrees) = h / 1 mile
To solve this equation for h, we need to find the value of tan(6 degrees).
By using a calculator or a trigonometric table, we find that tan(6 degrees) is approximately 0.1051.
Now we can plug in the value of tan(6 degrees) into the equation:
0.1051 = h / 1 mile
To isolate h, we can multiply both sides of the equation by 1 mile:
0.1051 * 1 mile = h
Therefore, the height of the building would be approximately 0.1051 miles.
To convert this height into a different unit, such as feet, you can use the appropriate conversion factor. For example, if there are 5,280 feet in a mile, you could multiply 0.1051 miles by 5,280 feet/mile to find the height in feet (approximately 555.408 feet).