Question

practice applying the law of sines. which expression gives the exact value of t? 21.3 sin(34°)/sin(118°) sin(34°)/21.3 sin(118°) 21.3 sin(118°)/sin(34°) 118 sin(34°)/sin(21.3°)

Explanation:

Step1: Find the measure of angle \( U \)

In a triangle, the sum of angles is \( 180^{\circ} \). So, \( \angle U=180^{\circ}-\angle S - \angle T\).
\(\angle U = 180^{\circ}-118^{\circ}-34^{\circ}=28^{\circ}\)

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 \(\triangle STU\), \(\frac{t}{\sin T}=\frac{SU}{\sin U}\). Here, \(SU = 21.3\), \(\angle T = 34^{\circ}\), \(\angle U=28^{\circ}\).
So, \(t=\frac{21.3\sin(34^{\circ})}{\sin(28^{\circ})}\)

Answer:

\(\frac{21.3\sin(34^{\circ})}{\sin(28^{\circ})}\)