Question

find s.
write your answer as an integer or as a decimal rounded to the nea
$s = \square$
submit

Explanation:

Step1: Find the third angle of the triangle

The sum of angles in a triangle is \(180^\circ\). Given angles at \(U\) is \(49^\circ\) and at \(S\) is \(110^\circ\), so the angle at \(T\) (\(\angle T\)) is \(180 - 49 - 110 = 21^\circ\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{s}{\sin S}=\frac{US}{\sin T}\). Here, \(US = 5\), \(\angle S = 110^\circ\), \(\angle T = 21^\circ\). So we have \(\frac{s}{\sin 110^\circ}=\frac{5}{\sin 21^\circ}\).

Step3: Solve for \(s\)

First, calculate \(\sin 110^\circ\approx0.9397\) and \(\sin 21^\circ\approx0.3584\). Then \(s=\frac{5\times\sin 110^\circ}{\sin 21^\circ}=\frac{5\times0.9397}{0.3584}\approx\frac{4.6985}{0.3584}\approx13.1\).

Answer:

\(13.1\)