Final answer:
sin ∠MQP = sin(56 degrees) The sine of angle MQP, represented as sin ∠MQP, equals the sine of 56 degrees.
Step-by-step explanation:
The sine of angle MQP, represented as sin ∠MQP, equals the sine of 56 degrees. This is the direct answer to the question.
In a right triangle MNR with a right angle at vertex M, angle R measures 34 degrees, and angle N measures 56 degrees, forming a right angle at M. Given that angle MQP measures 56 degrees, it's important to note that the sine function in trigonometry is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
In this scenario, as angle MQP is opposite angle N in the right triangle MNR, sin ∠MQP = sin(angle N) = sin(56 degrees). This implies that the ratio of the side opposite angle N to the hypotenuse remains constant in the given triangle, and therefore, the sine of angle MQP is equivalent to the sine of angle N, which is 56 degrees.
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