Question

find s.
write your answer as an integer or as a decimal rounded to the nearest ten
s =
submit
work it out

Explanation:

Step1: Find the third angle in triangle \( RST \)

The sum of angles in a triangle is \( 180^\circ \). Given \( \angle R = 127^\circ \) and \( \angle S = 24^\circ \), we find \( \angle T \) as follows:

$$ \angle T = 180^\circ - 127^\circ - 24^\circ = 29^\circ $$

Step2: Apply the Law of Sines

The Law of Sines states that in any triangle, \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \). In triangle \( RST \), we have side \( ST = 21 \) opposite \( \angle R = 127^\circ \), and side \( s \) (which is \( RT \)) opposite \( \angle S = 24^\circ \). So we set up the proportion:

$$ \frac{s}{\sin 24^\circ} = \frac{21}{\sin 127^\circ} $$

Step3: Solve for \( s \)

First, we know that \( \sin 127^\circ=\sin(180^\circ - 53^\circ)=\sin 53^\circ\approx0.7986 \) and \( \sin 24^\circ\approx0.4067 \).
We can re - arrange the proportion from Step 2 to solve for \( s \):

$$ s=\frac{21\times\sin 24^\circ}{\sin 127^\circ} $$

Substitute the values of the sines:

$$ s=\frac{21\times0.4067}{0.7986} $$

$$ s=\frac{8.5407}{0.7986}\approx10.7 $$

Answer:

\( s\approx10.7 \)