Question

Бічне ребро правильної трикутної піраміди дорівнює L А плоский кут при її вершині дорівнює а . знайти сторону основи піраміди. з малюнком ! швидше ! будь ласка!!!

Answer 1

Solution:

To find the length of the base side of the pyramid, we can use trigonometric functions and the given information about the lateral edge and the angle at the vertex.

Let's denote the length of the base side as b, the lateral edge as L, and the angle at the vertex as a.

Using trigonometric functions, we can relate the lateral edge, the base side, and the angle at the vertex as follows:

sin(a) = b / (L / 2)

Where: - sin(a) is the sine of the angle at the vertex. - b is the length of the base side. - L / 2 is half of the lateral edge, which forms a right-angled triangle with the base side.

By rearranging the equation, we can solve for b:

b = (L / 2) * sin(a)

Now, let's calculate the length of the base side using the given values.

Given: - L = {{L}} - a = {{a}}

Substitute the given values into the equation:

b = ({{L}} / 2) * sin({{a}})

Calculation:

b = ({{L}} / 2) * sin({{a}})

Result:

The length of the base side of the pyramid is b = ({{L}} / 2) * sin({{a}}).

This formula allows us to find the length of the base side of the pyramid based on the given lateral edge and the angle at the vertex.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.