Question

What is the measure of angle R shown below, given r = 10, q = 20, and Q = 100°? Round the answer to the nearest tenth.0.5° 2.0° 29.5° 50.5°

Answer 1

Answer : 29.5°

Given r = 10, q = 20, and Q = 100°

From the attached figure we can see that two sides and one angle is given

We use sine rule to find angle R

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

In triangle QRS

$\frac{sin Q}{q} = \frac{Sin R}{r} = \frac{Sin S}{s}$

r = 10, q = 20, and Q = 100°

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

Replace all the values

$\frac{sin 100}{20} = \frac{sin R}{10}$

$\frac{sin(100)*10}{20} = sin(R)$

$\frac{0.984807753*10}{20}$ =sin R

0.4932403876 = sin (R)

R= $sin^{-1} (0.4932403876)$

R= 29.5 degrees