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In triangle OPQ, if Q = 75 cm, ∠O = 113°, and ∠P = 18°, find the length of side O, to the nearest centimeter.

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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.

User J Atkin
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