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.

Using the law of the sine we have:

(sine (34) / 42) = (sine (x) / 61)

From here, we clear the value of x.

We have then:

sine (x) = (61/42) * (sine (34))

We apply the inverse to both sides:

Arcosine (sine (x)) = Arcosine ((61/42) * (sine (34)))

We get then:

x = Arcosine ((61/42) * (sine (34)))

x = 54.3 degrees

Answer:

m∠X = 54.3