Given: m∠ABC = 50°,
AC = 30
Find: OA

OA = 19.58

Step-by-step explanation:

If we draw the segments OA and OC, we will have an isosceles triangle OAC.

With the property of inscribed angles and central angles that are related to the same arc of the circunference, we have:

mAOC = 2 * mABC

mAOC = 2 * 50 = 100°

As the triangle OAC is isosceles, we have that mOAC = mACO.

Knowing that the sum of internal angles of a triangle is 180°, we have:

mACO + mOAC + 100 = 180

2 * mACO  = 80

mACO = 40°

Now, using the law of sines, we have:

OA / sin(ACO) = AC / sin(AOC)

OA / 0.6428 = 30 / 0.9848

OA = 30.463 * 0.6428 = 19.58

5/12, or 5: 12

step-by-step explanation: