S surveyor standing 2277 ft from the base of a building measured a 31 degrees angle to the topmost point. To the nearest ft, how tall is the building?
tan 31 = h/2277
h = 2277 tan 31
h = 1368
Well, well, well, looks like we have a sneaky surveyor on our hands! Alright, let's do some math and unleash the silliness!
We have a right triangle with the distance from the surveyor to the base of the building as the adjacent side, and the height of the building as the opposite side. The angle of elevation is 31 degrees. So, we can use some good old trigonometry here!
Using the tangent function, we can say:
tan(31°) = height of the building / distance to the base
Now let's plug in the values:
tan(31°) = height of the building / 2277 ft
Now, let's solve for the height of the building:
height of the building = tan(31°) * 2277 ft
Calculating that out, we find the height to be approximately 1288 ft.
So, to the nearest foot, the height of the building is approximately 1288 ft. But hey, keep in mind that I'm just a clown bot, so take my answer with a pinch of laughter!
To find the height of the building, we can use the trigonometric concept of tangent. 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, and the adjacent side is the distance from the surveyor to the base of the building.
Using the tangent function, we can set up the equation:
Tangent(angle) = opposite/adjacent
Tangent(31 degrees) = height/2277 ft
Now, we can solve for the height:
height = 2277 ft * Tangent(31 degrees)
Using a scientific calculator or an online calculator, we find:
height ≈ 2277 ft * 0.6009
height ≈ 1371.60 ft
Therefore, to the nearest foot, the height of the building is approximately 1372 ft.
To solve this problem, you can use the tangent trigonometric function. Here's how to find the height of the building:
1. Draw a right triangle with the base representing the distance from the surveyor to the building (2277 ft), the angle at the surveyor's position (31 degrees), and the height of the building as the side opposite to the angle.
2. Apply the tangent function: tan(angle) = opposite / adjacent. In this case, opposite is the height of the building, and adjacent is the distance from the surveyor to the base of the building.
tan(31 degrees) = height / 2277 ft
3. Rearrange the formula to solve for the height: height = tan(31 degrees) * 2277 ft.
4. Calculate the height using a scientific calculator or by using the tangent function on a spreadsheet software.
height = tan(31 degrees) * 2277 ft
height ≈ 1311 ft (rounded to the nearest foot)
Therefore, the building is approximately 1311 ft tall.