Using the Law of Sines in Δ PQR, that is
Given ∠ P, ∠ R and p then side r can be found
= , substitute values
= ( cross- multiply )
r sin27° = 9.5 sin135° ( divide both sides by sin27° )
r = ≈ 14.8 ( to 1 dec. place
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
The triangle has been drawn in the figure attached to this response.
From the triangle, applying sine rule gives;
= = --------------(i)
p = 9.5 units
∠P = 27°
∠R = 135°
Substituting these values into equation (i) gives;
= = --------------(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 ;
= [cross multiply]
9.5sin 135° = r sin 27°
9.5 x 0.7071 = r x 0.4540
6.717 = 0.4540r
r = 14.80 units
the answer is 13/48