What is the length of line segment RS? Use the law of sines to find the answer. Round to the nearest tenth. Law of sines:

Mathematics

2 answers:

Leno4ka [110]3 years ago

7 0

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:

$\frac{Sin(A)}{a} = \frac{Sin (B)}{b} = \frac{Sin (C)}{c}$

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:

$\frac{Sin (R)}{r} = \frac{Sin (S)}{s}\\ \frac{Sin (80)}{3.1} = \frac{Sin (S)}{2.4} \\Sin (S) = \frac{Sin (80)}{3.1} * 2.4\\Sin (S) = 0.762\\S = Sin^{-1} (0.762) \\S = 49.68$ °

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: $\frac{Sin (R)}{r} = \frac{Sin (Q)}{q}\\\frac{Sin (80)}{3.1} = \frac{Sin (50.32)}{RS}\\0.3177 = \frac{0.77}{RS}\\RS = 2.42 Units$