Question

If XY=16, XZ=14, JQ=6, and the radius of the circumscribed circle of triangle XYZ is 10, find QK

Answer 1

Check the picture below.

Answer 2

The length of QK is 7.1.

Law of Cosines:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we are looking for the length of QK, which is side c. We know that side XY is 16 and side XZ is 14. We also know that the angle between XY and XZ is 90 degrees (since they are perpendicular).

Therefore, we can plug in the following values into the Law of Cosines:

c^2 = 16^2 + 14^2 - 2 * 16 * 14 * cos(90)

c^2 = 576 + 196 = 772

c = sqrt(772) = 7.1

Therefore, the length of QK is 7.1.