Answer : 29.5°
Given r = 10, q = 20, and Q = 100°
From the attached figure we can see that two sides and one angle is given
We use sine rule to find angle R
[tex] \frac{sin A}{a} = \frac{Sin B}{b} = \frac{Sin C}{c} [/tex]
In triangle QRS
[tex] \frac{sin Q}{q} = \frac{Sin R}{r} = \frac{Sin S}{s} [/tex]
r = 10, q = 20, and Q = 100°
[tex] \frac{sin Q}{q} = \frac{Sin R}{r} [/tex]
Replace all the values
[tex] \frac{sin 100}{20} = \frac{sin R}{10} [/tex]
[tex] \frac{sin(100)*10}{20} = sin(R) [/tex]
[tex] \frac{0.984807753*10}{20} [/tex] =sin R
0.4932403876 = sin (R)
R= [tex] sin^{-1} (0.4932403876) [/tex]
R= 29.5 degrees
