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Margaret uses a rangefinder to measure various distances around a mountain canyon. Points P and R represent locations on one side of the canyon, and point Q represents a location on the other side of the canyon. Margaret measures the distances from point P to point R and from point R to point Q and finds them to be 50 feet and 122 feet, respectively. Given that the measure of ∠QPR is 96∘, what is the measure, in degrees, of ∠RQP?

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micahdisu

Answer: Angle RQP measures 24 degrees (approximately)

Step-by-step explanation: Please refer to the attached diagram for details. The dimensions taken by Margaret have eventually formed a triangle with one of the sides measuring 96 degrees and two sides measured as 50 and 122. Note that the side measuring 122 is facing the 96 degree angle. With this bit of information we shall apply the sine rule which states as follows;

a/SinA = b/SinB = c/SinC

We can now substitute for values,

122/Sin 96 = 50/Sin Q

By cross multiplication we now have

Sin Q = (50 x Sin 96)/122

Sin Q = (50 x 0.9945)/122

Sin Q = 49.73/122

Sin Q = 0.4076

Checking with your calculator or table of values,

Q = 24.05

Approximately angle RQP measures 24 degrees

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