Question

PLEASE HELP!!!

Answer 1

The measure of angle R is : 41.5°

what are trigonometric ratios?

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,

$q^{2}$ = $s^{2}$ + $r^{2}$ -2srcosQ

$q^{2}$ = $(30.6)^{2}$ + $(24.4)^{2}$ -2 x 30.6 x 24.4cos15

$q^{2}$ = 936.6 + 595.36 -1493.3(0.9659)

q = 9.5

using sine rule,

$\frac{24.4}{sin R}$ = $\frac{9.5}{sin 15}$

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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