Option A:
R = 109°
Solution:
Given data:
p = 31 cm, r = 67 cm and ∠P = 26°
To find the measure of angle R.
Using law of sines,
[tex]$\frac{\sin P}{p}=\frac{\sin R}{r}[/tex]
[tex]$\frac{\sin 26}{31}=\frac{\sin R}{67}[/tex]
Switch the sides.
[tex]$\frac{\sin R}{67}=\frac{\sin 26}{31}[/tex]
Multiply by 67 on both sides, we get
[tex]$\sin R=\frac{\sin 26}{31} \times 67[/tex]
sin R = 0.9474
[tex]R= \sin^{-1}0.9474[/tex]
R =71.34 + 360n, 108.65+ 360n, for any integer n
Here R is an obtuse angle, so ignore 71.34.
R = 108.65°
R = 109°
Option A is the correct answer.
