Final answer:
To find the length of side O in triangle OPQ, use the Law of Sines and set up a proportion to solve for x.
Step-by-step explanation:
To find the length of side O in triangle OPQ, we can use the Law of Sines. The Law of Sines states that for any triangle, the ratio between the length of a side and the sine of the opposite angle is constant. In this case, we have:
Q = 75 cm (opposite ∠P)
∠O = 113° (opposite side O)
∠P = 18° (opposite side PQ)
Let's call the length of side O x:
Sin(113°)/75 = Sin(18°)/x
Cross-multiplying:
Sin(113°) * x = 75 * Sin(18°)
x = (75 * Sin(18°)) / Sin(113°)
Using a calculator to find the values of the sines and evaluating the expression, we find that x is approximately 26 cm.