Question

Диагональ боковой грани правильной треугольной призмы равна 12 см.Она наклонена к стороне основания под углом 60. Найти высоту призмы

Answer 1

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Answer 2

Calculation of the Height of the Prism

To find the height of the prism, we can use the given information about the diagonal of one of the lateral faces and the angle at which the prism is inclined to the base.

Let's denote the diagonal of the lateral face as d and the height of the prism as h.

From the given information, we have: - Diagonal of the lateral face (d) = 12 cm - Angle of inclination to the base = 60 degrees

To find the height of the prism, we can use trigonometric ratios. In this case, we can use the sine function.

The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

In this case, we can consider the diagonal of the lateral face as the hypotenuse and the height of the prism as the opposite side.

Using the sine function, we can write:

sin(60) = h / d

Simplifying the equation, we have:

h = d * sin(60)

Now, let's substitute the given values into the equation and calculate the height of the prism.

h = 12 cm * sin(60)

Using a calculator, we can find that the sine of 60 degrees is approximately 0.866.

h = 12 cm * 0.866

Calculating the value, we get:

h ≈ 10.392 cm

Therefore, the height of the prism is approximately 10.392 cm.

Please note that the calculations are based on the given information and assumptions about the shape of the prism.