# In a right triangular prism, the diagonal of the side face forms an angle of 30 degrees with

October 7, 2021 | education

| **In a right triangular prism, the diagonal of the side face forms an angle of 30 degrees with the side of the base and is exactly 4 cm. Find the volume of the prism.**

In a right-angled triangle CB1B, the leg BB1 lies opposite the angle 30, then its length will be equal to: BB1 = CB1 / 2 = 4/2 = 2 cm.

Determine the length of the BC leg.

Cos30 = BC / CB1.

BC = CB1 * Cos30 = 4 * √3 / 2 = 2 * √3 cm.

Since the prism is correct, an equilateral triangle lies at its base.

The area of a regular triangle is equal to: Sавс = ВС ^ 2 * √3 / 4 = (2 * √3) ^ 2 * √3 / 4 = 12 * √3 / 4 = 3 * √3 cm2.

Let’s define the volume of the prism.

Vprice = Saavs * BB1 = 3 * √3 * 2 = 6 * √3 cm3.

Answer: The volume of the prism is 6 * √3 cm3.

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