Question

question in \\( \delta v w x, v = 9.1 \\) inches, \\( x = 7.2 \\) inches and \\( \angle x = 129 ^ { \circ } \\). find all possible values of \\( \angle v \\), to the nearest 10th of a degree. answer attempt 1 out of 2 additional angle no possible angles

Explanation:

Step1: Use the Law of Sines

The Law of Sines states that \(\frac{\sin V}{v}=\frac{\sin X}{x}\).
Substitute \(v = 9.1\), \(x=7.2\), and \(\angle X = 129^{\circ}\) into the formula: \(\sin V=\frac{v\sin X}{x}\).
So, \(\sin V=\frac{9.1\times\sin(129^{\circ})}{7.2}\).
First, calculate \(\sin(129^{\circ})\approx0.777\).
Then, \(\sin V=\frac{9.1\times0.777}{7.2}\approx\frac{7.07}{7.2}\approx0.982\).

Step2: Find the angle \(V\)

Since \(\sin V\approx0.982\), \(V=\sin^{- 1}(0.982)\approx79.2^{\circ}\).
Check for the supplementary angle: \(180^{\circ}-79.2^{\circ} = 100.8^{\circ}\). But \(100.8^{\circ}+129^{\circ}=229.8^{\circ}>180^{\circ}\), so we discard it.

Answer:

\(79.2^{\circ}\)