Question

What is the measure of angle R?

Answer 1

Option B:

25 degrees

Solution:

Given data in triangle PQR,

The side opposite to angle P is p.

The side opposite to angle Q is q.

The side opposite to angle R is r.

q = 36, r = 20, angle Q = 50°.

To find the measure of angle R:

Using law of sine,

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

$\Rightarrow\frac{p}{\sin P}=\frac{q}{\sin Q}=\frac{r}{\sin R}$

Take only two sides.

$\Rightarrow\frac{q}{\sin Q}=\frac{r}{\sin R}$

Substitute the given values.

$\Rightarrow\frac{36}{\sin 50^\circ}=\frac{20}{\sin R}$

Do cross multiplication.

$\Rightarrow36\times\sin R = \sin50^\circ\times20$

sin 50° = 0.766

$\Rightarrow36\times\sin R = 0.766\times20$

$\Rightarrow36\times\sin R = 15.32$

$\Rightarrow\sin R = \frac{15.32}{36}$

$\Rightarrow\sin R = 0.4255$

$\Rightarrow R = \sin^{-1}(0.4255)$

⇒ R = 25.18°

⇒ R = 25° (approximately)

Option B is the correct answer.

Hence the measure of angle R is 25 degrees.