the lateral edge of side 12 makes an angle of 30 degrees with the base, what is the altitude of the square prism?
To find the altitude of the square prism, we can use trigonometry. Let's break it down step by step:
Step 1: Understand the problem.
In a square prism, the base is a square, and the lateral edge is perpendicular to the base. We are given that the lateral edge makes an angle of 30 degrees with the base. We need to find the altitude, which is the length of the perpendicular line from the base to the top of the prism.
Step 2: Identify the relevant trigonometric function.
In this problem, we know the angle (30 degrees) and the length of the side of the base (12 units). The trigonometric function that relates the angle, side length, and altitude is the tangent function (tan).
Step 3: Apply the trigonometric function.
The tangent function is defined as the ratio of the length of the side opposite the angle (in this case, the altitude) to the length of the side adjacent to the angle (in this case, the lateral edge). So we have:
tan(30 degrees) = altitude / 12
Step 4: Solve for the altitude.
We need to isolate the altitude to find its value. To do this, we can multiply both sides of the equation by 12:
12 * tan(30 degrees) = altitude
Now, we can calculate the value using a calculator:
12 * tan(30 degrees) ≈ 6.93
Therefore, the altitude of the square prism is approximately 6.93 units.