Answer:
The length of side r can be found using sine rule (Law of sines).
This gives side r a length value of 14.80 units
Step-by-step explanation:
The triangle has been drawn in the figure attached to this response.
From the triangle, applying sine rule gives;
[tex]\frac{p}{sinP}[/tex] = [tex]\frac{q}{sinQ}[/tex] = [tex]\frac{r}{sinR}[/tex] --------------(i)
But;
p = 9.5 units
∠P = 27°
∠R = 135°
Substituting these values into equation (i) gives;
[tex]\frac{9.5}{sin 27^0}[/tex] = [tex]\frac{q}{sin Q}[/tex] = [tex]\frac{r}{sin 135^0}[/tex] --------------(ii)
From equation (ii), since no details about q or Q has been given, then it is difficult and impossible to calculate the length of q or the angle Q using the sine rule. Therefore, the length that can be determined is that of r since the value of angle R is given.
Then, equation (ii) reduces to ;
[tex]\frac{9.5}{sin 27^0}[/tex] = [tex]\frac{r}{sin 135^0}[/tex] [cross multiply]
9.5sin 135° = r sin 27°
9.5 x 0.7071 = r x 0.4540
6.717 = 0.4540r
r = [tex]\frac{6.717}{0.4540}[/tex]
r = 14.80 units
