Answer:
The values of [tex]\bf\angle S=17.53^o\ or\ 162.47^o[/tex].
Step-by-step explanation:
We can find the values of angle S of ΔRST by using the sine rule:
[tex]\boxed{for\ \Delta ABC\ applies:\frac{a}{sin\angle A} =\frac{b}{sin\angle B}=\frac{c}{sin\angle C} }[/tex]
Given:
Therefore:
[tex]\displaystyle\frac{r}{sin\angle R} =\frac{s}{sin\angle S}[/tex]
[tex]\displaystyle\frac{87}{sin\ 76^o} =\frac{27}{sin\angle S}[/tex]
[tex]\displaystyle sin\angle S=\frac{27\times sin\ 76^o}{87}[/tex]
[tex]sin\angle S=0.3011[/tex]
[tex]\bf\angle S=17.53^o\ or\ 162.47^o[/tex]
