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SpyIntel [72]
3 years ago
14

What is the measure (in radians) of central angle theta in the circle below? enter an exact expression.

Mathematics
1 answer:
Llana [10]3 years ago
6 0

Answer:

Measure of central angle is 3.665 radians

Step-by-step explanation:

In this question, we are trying to get the value of the central angle.

As we can see, the radius of the circle is 12cm while the length of the major arc is 14 pi cm.

Mathematically the length of an arc is calculated as follows;

Length of arc = theta/360 * 2 * pi * r

Plugging the values we have from the question;

14 pi = theta/360 * 2 * pi * 12

divide both sides by 2pi

7 = theta/360 * 12

360 * 7 = 12 theta

theta = (360 * 7)/12

theta = 210

Since 1 degree = pi/180 radian

it means 210 degrees = 210 * pi/180 = 3.665 radians

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The computation shows the radius of the circle that is inscribed in the isosceles triangle will be 3.33cm.

<h3>How to calculate the radius?</h3>

From the information given, the isosceles triangle the length of a base is 10 cm and the length of a leg is 13 cm.

Let A = area of the triangle

Let S = semi perimeter of the triangle.

The radius will be: = A/S

where,

S = \dfrac{(a + b + c)}{2} = \dfrac{(13 + 13 + 10)}{2} = 18

The radius will be:

 =\dfrac{(\sqrt{18} - \sqrt{13})(\sqrt{18} - \sqrt{13})(\sqrt{18} - \sqrt{10})} { 18}

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In conclusion, the radius is 3.33cm.

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