Question

triangle PQR with side p across from angle P, side q across from angle Q, and side r across from angle R If ∠P measures 27°, ∠R measures 135°, and p equals 9.5, then which length can be found using the Law of Sines?

Answer 1

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;

$\frac{p}{sinP}$ = $\frac{q}{sinQ}$ = $\frac{r}{sinR}$            --------------(i)

But;

p = 9.5 units

∠P = 27°

∠R = 135°

Substituting these values into equation (i) gives;

$\frac{9.5}{sin 27^0}$ = $\frac{q}{sin Q}$ = $\frac{r}{sin 135^0}$            --------------(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 ;

$\frac{9.5}{sin 27^0}$ = $\frac{r}{sin 135^0}$        [cross multiply]

9.5sin 135° = r sin 27°

9.5 x 0.7071 = r x 0.4540

6.717 = 0.4540r

r = $\frac{6.717}{0.4540}$

r = 14.80 units