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To find the missing value, we can use the inverse sine function (sin⁻¹).
sin⁻¹(8/15) ≈ 0.627
When we convert this value to degrees, it will be approximately 35.86°.
Therefore, the missing value to the nearest hundredth is 35.86°.
None of the given options is exactly 35.86°, but the closest option is 32.23°.