Question

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:

A. 2.2 units
B. 2.4 units
C. 3.0 units
D. 3.3 unit

Answer 1

Correct Answer is B. 2.4 Units

Explanation:

The missing picture in question is attached.

The Law of Sines is given as:

`(Sin(A))/(a) = (Sin (B))/(b) = (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:

`(Sin (R))/(r) = (Sin (S))/(s)\\ (Sin (80))/(3.1) = (Sin (S))/(2.4) \\Sin (S) = (Sin (80))/(3.1) * 2.4\\Sin (S) = 0.762\\S = Sin^(-1) (0.762) \\<strong>S = 49.68</strong>`°

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:
`(Sin (R))/(r) = (Sin (Q))/(q)\\(Sin (80))/(3.1) = (Sin (50.32))/(RS)\\0.3177 = (0.77)/(RS)\\RS = <strong>2.42 Units</strong>`