find $m\\angle x$.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$m\\angle…

find $m\\angle x$.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$m\\angle x = \\square^\\circ$

find $m\\angle x$.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$m\\angle x = \\square^\\circ$

Answer

Explanation:

Step1: Identify sides relative to ∠X

In right triangle (XYZ), (\angle Y = 90^\circ). For (\angle X):

  • Opposite side: (YZ = 2)
  • Hypotenuse: (XZ = 3)

Step2: Use sine function for ∠X

Sine of an angle is (\frac{\text{opposite}}{\text{hypotenuse}}). (\sin(\angle X) = \frac{2}{3})

Step3: Calculate ∠X with arcsine

Take inverse sine to find the angle. (\angle X = \arcsin\left(\frac{2}{3}\right)) Calculate the value: (\arcsin\left(\frac{2}{3}\right) \approx 41.8^\circ)

Answer:

(41.8^\circ)