The measure of angle R is : 41.5°
Trigonometric ratios are ratios of the sides of a right-angled triangle.
They are used to relate the sides of a triangle with their angles.
Examples are cosine, tangent, sine etc.
Analysis:
length r is facing angle R, length s is facing angle S, length q is facing angle Q.
in order to find angle R we need to find the length of q first.
using cosine rule,
[tex]q^{2}[/tex] = [tex]s^{2}[/tex] + [tex]r^{2}[/tex] -2srcosQ
[tex]q^{2}[/tex] = [tex](30.6)^{2}[/tex] + [tex](24.4)^{2}[/tex] -2 x 30.6 x 24.4cos15
[tex]q^{2}[/tex] = 936.6 + 595.36 -1493.3(0.9659)
q = 9.5
using sine rule,
[tex]\frac{24.4}{sin R}[/tex] = [tex]\frac{9.5}{sin 15}[/tex]
9.5 sinR = 24.4sin15
sin R = 24.4(0.2588)
sin R = 6.31
R = arc(sin) 6.31 = 41.5°
In conclusion, the measure of angle R is 41.5°
Learn more about trigonometric ratios: brainly.com/question/24349828
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