Question

В конусе образующая равна 15 см и составляет с основанием угол 60 градусов. найдите радиус описанной окружности

Answer 1

R=a*30°=15*0.5=7.5см

Ответ: 7.5см.

Answer 2

Finding the Radius of the Circumscribed Circle in a Cone

To find the radius of the circumscribed circle in a cone, we need to use the given information about the cone's slant height and the angle between the slant height and the base.

Given: - The length of the slant height (the height of the cone) is 15 cm. - The angle between the slant height and the base is 60 degrees.

To find the radius of the circumscribed circle, we can use trigonometric ratios. Specifically, we can use the sine function.

The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the side opposite the angle is the radius of the circumscribed circle, and the hypotenuse is the slant height of the cone.

Using the sine function, we can write the following equation:

sin(60 degrees) = radius / slant height

Let's solve for the radius:

radius = slant height * sin(60 degrees)

Substituting the given values:

radius = 15 cm * sin(60 degrees)

To calculate the value of sin(60 degrees), we can refer to the trigonometric values of common angles. The sine of 60 degrees is equal to 0.866.

radius = 15 cm * 0.866

Calculating the result:

radius ≈ 12.99 cm

Therefore, the radius of the circumscribed circle in the given cone is approximately 12.99 cm.

Please note that the result is rounded to two decimal places.