Question

consider a triangle abc like the one below. suppose that c = 14, a = 54, and c = 108°. (the figure is not drawn to scale.) solve the triangle.
carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
if no such triangle exists, enter
o solution.\ if there is more than one solution, use the button labeled \or\.
a = □°, b = □°, b = □

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{c}{\sin C}\). Substituting the given values \(a = 54\), \(c=14\), and \(C = 108^{\circ}\), we get \(\frac{54}{\sin A}=\frac{14}{\sin 108^{\circ}}\). Then \(\sin A=\frac{54\sin 108^{\circ}}{14}\).
Calculate \(\sin 108^{\circ}\approx0.9511\), so \(\sin A=\frac{54\times0.9511}{14}\approx\frac{51.3594}{14}\approx3.6685\).
Since the range of the sine function is \([- 1,1]\), and \(3.6685>1\).

Answer:

No solution