Question

в правильной треугольной пирамиде боковое ребро равно 6 и образует с основанием угол 30. Найти сторону основания?

Answer 1

Finding the Side Length of the Base of a Right Triangular Pyramid

To find the side length of the base of a right triangular pyramid, we can use the given information that the lateral edge is equal to 6 and forms a 30-degree angle with the base.

Let's denote the side length of the base as x.

To solve for x, we can use trigonometric ratios. In this case, we can use the sine function because we have the opposite side (the lateral edge) and the angle between the lateral edge and the base.

The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the hypotenuse is the lateral edge.

Using the sine function, we can write the equation:

sin(30) = x / 6

To solve for x, we can multiply both sides of the equation by 6:

6 * sin(30) = x

Now, let's calculate the value of x using the given information.

The sine of 30 degrees is 0.5. Therefore:

x = 6 * 0.5 = 3

So, the side length of the base of the right triangular pyramid is 3.