The lateral edges of edge 8m of an oblique square prism is inclined at an angle of 30 degrees with the altitude. What is the altitude of the prism?...

To find the altitude of the prism, we need to understand the geometry of an oblique square prism.

First, let's clarify a few terms. The base of a square prism is a square, and the altitude is the perpendicular distance between the two parallel bases. The lateral edges are the vertical edges connecting the corresponding vertices of the bases.

Given that the lateral edges of the prism are inclined at an angle of 30 degrees with the altitude, we can use trigonometry to find the altitude.

Let's label the altitude as "h."

Since the lateral edges are inclined at a 30-degree angle with the altitude, we can use the sine function. The sine of an angle is equal to the opposite side divided by the hypotenuse.

In this case, the opposite side is half the length of the lateral edge, which is 4m (half of 8m). The hypotenuse is the altitude, h.

So, we have sin(30°) = 4m / h.

The sine of 30 degrees is 1/2, so the equation becomes 1/2 = 4m / h.

To solve for h, we can cross-multiply and then divide:

1*h = 2*4m
h = 8m

Therefore, the altitude of the prism is 8 meters.