a boy walks 50m from the bottom of a building lies down and notes that he has to raise his eyes through 42 degree from the horizontal. what is the height of the building?
i am doing tan(42)=x/50 but the answer is supposed to be 45m. how do i get that?
actually don't answer that im stupid. i hand by calculator in rad rather than deg. sorry. have a great rest of the day.
Good, only those who don't work never make mistakes!
To find the height of the building, we can use trigonometry. You were correct in using the tangent function (tan) to solve the problem. However, there might have been a mistake in your calculations.
Let's break down the problem and explain it step by step:
1. The boy walked 50m from the bottom of the building and lies down, forming a right triangle.
2. The angle between the horizontal and the line of sight from the boy to the top of the building is 42 degrees, as noted in the question.
3. The height of the building represents the opposite side of the triangle.
4. We need to find the length of the opposite side, which is the height of the building.
Here's how you can correctly calculate the height of the building:
1. Use the tangent function (tan) to find the ratio between the opposite side (height of the building) and the adjacent side (distance from the boy to the building).
tan(42) = Opposite / Adjacent
tan(42) = height / 50
2. Rearrange the equation to solve for the height:
height = tan(42) * 50
Now, let's calculate the height using this equation:
Using a calculator or math software, calculate tan(42) to find the tangent of 42 degrees:
tan(42) ≈ 0.9004040443 (approximately)
Multiply the tangent by 50:
height ≈ 0.9004040443 * 50
height ≈ 45.02 m (approximately)
Therefore, the height of the building is approximately 45.02 meters, which confirms the expected answer of 45 meters.