In a triangle ABC AC = 11 BC = √135 angle C = 90 Find the radius of the circumscribed circle.
September 20, 2021 | education
| In the ABC triangle it is known:
Leg AC = 11;
BC leg = √135;
Angle C = 90 °.
Find the radius of the circumscribed circle.
1) In a right-angled triangle, the radius of the circumscribed circle is half the hypotenuse.
2) Since 2 legs are known, then we find the hypotenuse of a right triangle by the Pythagorean theorem.
AB = √ (AC ^ 2 + BC ^ 2);
Substitute the known values and calculate the hypotenuse of the right triangle.
AB = √ (11 ^ 2 + √135 ^ 2) = √ (121 + 135) = √256 = √16 ^ 2 = 16.
3) Find the radius of the circumscribed circle. To do this, divide the hypotenuse of a right-angled triangle by 2.
16/2 = 2 * 8/2 = 1 * 8/1 = 8/1 = 8.
This means that the radius of the circumscribed circle around a right-angled triangle is 8.
Answer: 8.
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