Question

find s.
write your answer as an integer or as a decimal rounded to the nearest tenth.
s =

Explanation:

Step1: Find the third angle of the triangle

The sum of angles in a triangle is \(180^\circ\). Given \(\angle S = 43^\circ\) and \(\angle Q = 95^\circ\), we find \(\angle R\) as follows:
\(\angle R=180^\circ - 43^\circ - 95^\circ=42^\circ\)

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\) for a triangle with sides \(a,b,c\) and opposite angles \(A,B,C\) respectively.
In \(\triangle SQR\), we have \(\frac{s}{\sin S}=\frac{SR}{\sin Q}\). Here, \(SR = 16\), \(\angle S=43^\circ\), \(\angle Q = 95^\circ\).
So, \(s=\frac{16\times\sin43^\circ}{\sin95^\circ}\)

Step3: Calculate the values

We know that \(\sin43^\circ\approx0.682\) and \(\sin95^\circ\approx0.996\)
\(s=\frac{16\times0.682}{0.996}=\frac{10.912}{0.996}\approx10.95\approx11.0\) (rounded to the nearest tenth)

Answer:

\(11.0\)