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:

`(sin(Z))/(z)=(sin(X))/(x) \\ \\(sin(34))/(42)=(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