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1 Answer
- az_lenderLv 71 year ago
Angle BAC = arctan(2/6) = 18.435 degrees.
AC = sqrt(36+4) = 2*sqrt(10).
(1/2)AC = sqrt(10).
Angle OAC = arccos{sqrt(10)/[5*sqrt(2)]}
= arccos[sqrt(5)/5] = 63.435 degrees.
Therefore angle OAB = 63.435 - 18.435 = 45 degrees.
Although that doesn't look quite right, notice that the drawing must be the wrong shape anyway, because the radius is supposed to be around 7.07, while AB is only 6, and so the drawing is not accurate.
Going with the given numbers, use the cosine law:
OB^2 = AB^2 + OA^2 - 2(OA)(AB)cos(<OAB)
= 36 + 50 - 60*sqrt(2)*cos(45 deg)
= 86 - 44.575 = 41.425, and
OB = sqrt(41.425) = 6.436.
