Final answer:
To find the length of q, use the Law of Cosines with the given information.
Step-by-step explanation:
To find the length of q, we can use the Law of Cosines. Let's label the sides of the triangle formed by A, O, and P as a = 6.3 cm, b = q, and c = p.
The Law of Cosines states that c^2 = a^2 + b^2 - 2ab cos(C), where C is the angle opposite side c.
Plugging in the values, we get (6.3)^2 = q^2 + (6.3)^2 - 2q(6.3)cos(149°).
Solving this equation for q will give us the length of q, to the nearest tenth of a centimeter.