Just really quick, my friend and I disagree on this problem. I got 1997 and he got 721.033
4. A surveryor is standing on horizontal ground level with the base of a skyscraper. The angle formed by the line segment from his position to the top of the skyscraper is 31 degrees. The height of the building is 1200 feet. Find the distance from the building to the surveyor to the nearest foot.
Who's right?
Never mind everyone. I graphed it and showed him I was correct.
To solve this problem, we can use trigonometry. In particular, we can use the tangent function to find the distance from the building to the surveyor.
Here's how to do it:
1. First, we need to draw a diagram of the situation. Draw a horizontal line to represent the ground, and from one end of the line draw a vertical line to represent the skyscraper. Label the angle between the ground and the line segment to the top of the skyscraper as 31 degrees.
2. Since we know the height of the building is 1200 feet, we can label this distance on our diagram.
3. Now we can use the tangent function (tan) to find the distance from the building to the surveyor. The formula for tangent is tan(angle) = opposite/adjacent. In this case, the angle is 31 degrees, the opposite side is the height of the building (1200 feet), and the adjacent side is the distance we want to find.
4. Rearranging the formula, we have distance = opposite / tan(angle).
5. Plugging in the values, we get distance = 1200 / tan(31).
6. Now we can calculate the distance using a calculator. Make sure your calculator is in degree mode, and then evaluate tan(31) to find its value. Divide 1200 by this value.
Using these steps, we can find that the distance from the building to the surveyor is approximately 1996.6 feet (rounding to the nearest foot).
Based on this calculation, it seems that you are correct with a distance of 1997 feet, while your friend's answer of 721.033 feet is incorrect.