Question

question
in \\( \delta xyz \\), \\( x = 770 \mathrm{cm} \\), \\( z = 280 \mathrm{cm} \\) and \\( \angle z = 22 ^ { \circ } \\). find all possible values of \\( \angle x \\), to the nearest degree.
answer attempt 1 out of 2
additional angle
no possible angles
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Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{\sin X}{x}=\frac{\sin Z}{z}\). Substituting the given values \(x = 770\), \(z=280\), and \(Z = 22^{\circ}\), we get \(\frac{\sin X}{770}=\frac{\sin22^{\circ}}{280}\).

Step2: Solve for \(\sin X\)

Cross - multiply: \(\sin X=\frac{770\times\sin22^{\circ}}{280}\). Calculate \(\sin22^{\circ}\approx0.3746\). Then \(\sin X=\frac{770\times0.3746}{280}\). \(770\times0.3746 = 288.442\), and \(\frac{288.442}{280}\approx1.03\). But \(\sin X\leqslant1\). Since \(1.03>1\), there are no possible values for \(\angle X\).

Answer:

No Possible Angles