Question

determine the remaining sides and angles of the triangle abc.
a = 104.95°, c = 39.33°, c = 250
b = 35.72°
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 \(A = 104.95^{\circ}\), \(C=39.33^{\circ}\), and \(c = 250\).
So, \(a=\frac{c\sin A}{\sin C}\).

Step2: Substitute the values

Substitute \(c = 250\), \(\sin A=\sin(104.95^{\circ})\), and \(\sin C=\sin(39.33^{\circ})\) into the formula.
\(\sin(104.95^{\circ})\approx0.967\), \(\sin(39.33^{\circ})\approx0.634\).
\(a=\frac{250\times0.967}{0.634}\).
First, calculate \(250\times0.967 = 241.75\).
Then, \(a=\frac{241.75}{0.634}\approx381.3\).

Answer:

\(a\approx381.3\)