Question

Найдите хорду, на которую опирается угол 30 градусов, вписанный в окружность радиуса 32

Answer 1

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Answer 2

Finding the Chord of a 30-Degree Inscribed Angle in a Circle

To find the chord on which a 30-degree angle is based, we can use the properties of inscribed angles in a circle.

The measure of an inscribed angle is half the measure of its intercepted arc. In this case, we have a 30-degree angle, which means the intercepted arc has a measure of 60 degrees.

To find the length of the chord, we need to know the radius of the circle. The given radius is 32.

Using the properties of a circle, we can calculate the length of the chord using the formula:

Chord Length = 2 * Radius * sin(angle/2)

Substituting the values, we have:

Chord Length = 2 * 32 * sin(30/2)

Calculating this, we get:

Chord Length = 2 * 32 * sin(15) Chord Length ≈ 2 * 32 * 0.2588 Chord Length ≈ 16.5248

Therefore, the chord on which the 30-degree angle is based has a length of approximately 16.5248.

Please note that the above calculation assumes the angle is measured in degrees. If the angle is measured in radians, the calculation would be different.