The range of lengths for the line segment PR is PR ∈ [19, 37].
In this problem we know the lengths of the first two line segments and that the third segment is related to the first two, not meaning necessarily that exists any form of collinearity, and therefore we have more than a answer. Then, we can concieve the line segment PR as a side of a triangle named PQR, and which can be modeled by the law of cosine:
PR = √(PQ² + QR² - 2 · PQ · QR · cos θ) (1)
Where θ is the angle opposite to the line segment PR and θ ∈ [0, 180].
The range for the lengths of the line segment PR are:
θ = 0°
PR = √(PQ² + QR² - 2 · PQ · QR)
PR = √(9² + 28² - 2 · 9 · 28)
PR = 19
θ = 180°
PR = √(PQ² + QR² + 2 · PQ · QR)
PR = √(9² + 28² + 2 · 9 · 28)
PR = 37
The range of lengths for the line segment PR is PR ∈ [19, 37].
To learn more on law of cosine: https://brainly.com/question/17289163
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