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

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