We have a right triangle formed by the building, the ground, and the measuring instrument. The angle of elevation (\(θ\)) is 30 degrees, and the height of the building (\(h\)) is 40 meters. We want to find the distance (\(d\)) from the instrument to the foot of the building.

Using trigonometry, we can use the tangent function to relate the angle of elevation to the sides of the triangle:

\(\tan(θ) = \frac{h}{d}\(

Plugging in the values we have:

\(\tan(30°) = \frac{40}{d}\(

We know that \(\tan(30°) = \frac{1}{√3}\), so we can rewrite the equation as:

\(\frac{1}{√3} = \frac{40}{d}\(

Solving for \(d\):

\(d = \frac{40}{√3}\(