If the angle of elevation of sun is 30 degrees from the horizontal line, then the length of the shadow cast by a building 50 m high is.

tan 20 = 50/x

tan = opp/adj.

To find the length of the shadow cast by the building, we can use trigonometry. Let's assume that the length of the shadow is "x" meters.

In this problem, the angle of elevation is the angle between the horizontal line and the line from the top of the building to the top of the shadow. Since we know the angle of elevation is 30 degrees, we can use the trigonometric function tangent (tan) to find the length of the shadow.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, the side opposite the angle is the height of the building (50 m), and the side adjacent to the angle is the length of the shadow (x m). Therefore, we have:

tan(30 degrees) = height of the building / length of the shadow
tan(30 degrees) = 50 / x

To solve this equation for x, we need to isolate x. We can do this by multiplying both sides of the equation by x:

x * tan(30 degrees) = 50

Now, we can solve for x by dividing both sides of the equation by tan(30 degrees):

x = 50 / tan(30 degrees)

Using a scientific calculator or a trigonometric table, we can find that the tangent of 30 degrees is approximately 0.577. Substituting this value into our equation, we get:

x = 50 / 0.577
x ≈ 86.60

Therefore, the length of the shadow cast by the building is approximately 86.60 meters.