The radius of a circle circumscribed about a triangle is 10 cm. Find the side of the triangle
| March 17, 2021 | education
The radius of a circle circumscribed about a triangle is 10 cm. Find the side of the triangle that lies opposite an angle of 30 degrees.
The side AB of triangle ABC in a circle is a chord. The length of the chord L can be calculated by the formula
L = 2 * R * sin (<AOB / 2); <AOB – center angle;
<AOB = 2 * <ACB, since <ACB is an inscribed angle based on the same arc as <AOB;
<AOB = 2 * 30 ° = 60 °;
L = 2 * R * sin (60 ° / 2) = 2 * R * sin 30 °;
sin 30 ° = 0.5;
L = 2 * 10 * 0.5 = 10 (cm).
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