Answer :

Based on the right-angled triangle shown above, the measure of angle R is equal to 28.07°.

In order to determine the trigonometric ratio for cos(R), we would have to apply the basic cosine trigonometric function because the given side lengths represent the adjacent side (QR) and hypotenuse (PR) of a right-angled triangle;

cos(θ) = Adj/Hyp

Where:

Adj represent the adjacent side of a right-angled triangle.

Hyp represent the hypotenuse of a right-angled triangle.

θ represent the angle.

By applying the cosine trigonometric ratio to right-angled triangle PQR, we have the following:

cosθ = adjacent side/hypotenuse

cos(R) = QR/PR

cos(R) = 15/17

[tex]R =cos^{-1}(0.88235294117647058823529411764706)[/tex]

R = 28.07°.

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