From a point 100m from the foot of a building, the angle of elevation of the top of the building is 18°42 Find the height of the building
We can start by drawing a diagram:
We know that the angle of elevation from the ground to the top of the building is 18°42'. We also know that the distance from the point on the ground to the building is 100m. From the diagram, we can see that the height of the building is the opposite side of the triangle formed by the ground, the building, and the line of sight to the top of the building. We can use trigonometry to find the height:
tan(18°42') = height / 100m
height = 100m * tan(18°42')
height = 33.7m (rounded to one decimal place)
Therefore, the height of the building is approximately 33.7m.
To find the height of the building, we can use trigonometry and the given angle of elevation.
Let's define the height of the building as "h".
Since we have the angle of elevation, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by 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 point to the foot of the building, which is 100m.
Therefore, we have:
tan(18°42) = h / 100
Now, let's calculate the height using this equation.
Using a scientific calculator, calculate the tangent of 18°42. The result is approximately 0.331.
Substituting this value into the equation:
0.331 = h / 100
To isolate "h", we can multiply both sides of the equation by 100:
100 * 0.331 = h
So, the height of the building is approximately:
h = 33.1 meters
Therefore, the height of the building is 33.1 meters.