Question

determine the remaining sides and angles of the triangle abc.
a = 119.66°, c = 22.38°, c = 220
b = 37.96°
a ≈ □
(do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Use the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{c}{\sin C}\).
We know \(A = 119.66^{\circ}\), \(C=22.38^{\circ}\), and \(c = 220\).
So, \(a=\frac{c\times\sin A}{\sin C}\).

Step2: Substitute the values

Substitute \(c = 220\), \(\sin A=\sin(119.66^{\circ})\approx0.868\), and \(\sin C=\sin(22.38^{\circ})\approx0.381\) into the formula.
\(a=\frac{220\times\sin(119.66^{\circ})}{\sin(22.38^{\circ})}=\frac{220\times0.868}{0.381}\).
First, calculate \(220\times0.868 = 190.96\).
Then, \(a=\frac{190.96}{0.381}\approx501.2\).

Answer:

\(a\approx501.2\)