Question

In △XYZ, m∠Z = 34, x = 61 cm, and z = 42 cm. Find m∠X. Round your answer to the nearest tenth of a degree.

Answer 1

m∠X = 54.3°.

Using the Law of Sines, we have:
$\frac{\sin{Z}}{z}=\frac{\sin{X}}{x} \\ \\\frac{\sin{34}}{42}=\frac{\sin{X}}{61}$

Cross multiplying gives us
61(sin 34) = 42(sin X)

Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X

Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X