Answer:
Correct Answer is B. 2.4 Units
Step-by-step explanation:
The missing picture in question is attached.
The Law of Sines is given as:
[tex]\frac{Sin(A)}{a} = \frac{Sin (B)}{b} = \frac{Sin (C)}{c}[/tex]
Where,
a,b,c are the length of sides of triangle
A,B,C are the angles between the two sides of triangle
According to the picture attached, we have ΔRQS,
Let,
r = 3.1 units
R = 80°
s = 2.4 units
S = S
q = RS
Q = Q
Using law of Sines:
[tex]\frac{Sin (R)}{r} = \frac{Sin (S)}{s}\\ \frac{Sin (80)}{3.1} = \frac{Sin (S)}{2.4} \\Sin (S) = \frac{Sin (80)}{3.1} * 2.4\\Sin (S) = 0.762\\S = Sin^{-1} (0.762) \\S = 49.68[/tex]°
Since, triangle is constitute of total 180°, hence,
∠Q + ∠R + ∠S = 180°
∠Q + 80 + 49.68 = 180
∠Q = 180 - 80 - 49.68
∠Q = 50.32°
To find line segment RS, again use law of sines:[tex]\frac{Sin (R)}{r} = \frac{Sin (Q)}{q}\\\frac{Sin (80)}{3.1} = \frac{Sin (50.32)}{RS}\\0.3177 = \frac{0.77}{RS}\\RS = 2.42 Units[/tex]
