Answer:
Law of sine
Angle R = 34°
Explanation:
From the question given above, the following data were obtained:
Side opposite angle Q (q) = 54 ft
Angle Q = 96 °
Side opposite angle R (r) = 30 ft
Angle R =?
The value of angle R can be obtained by using the law of sine as illustrated below:
r / Sine R = q / Sine Q
30 / Sine R = 54 / Sine 96
Cross multiply
54 × Sine R = 30 × Sine 96
54 × Sine R = 30 × 0.9945
54 × Sine R = 29.835
Divide both side by 54
Sine R = 29.835 / 54
Sine R = 0.5525
Take the inverse of Sine
R = Sine¯¹ 0.5525
R = 34°
Thus, the value of angle R is 34°