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$m\\angle x = \\square^\\circ$\nsubmit

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

Answer

Explanation:

Step1: Identify triangle sides

Right triangle at $Z$: $YZ=7$, $XY=10$, $XZ=?$ First calculate $XZ$ via Pythagoras: $$XZ = \sqrt{XY^2 - YZ^2} = \sqrt{10^2 - 7^2} = \sqrt{100-49} = \sqrt{51} \approx 7.141$$

Step2: Use sine for $\angle X$

$\sin(\angle X) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{YZ}{XY}$ $$\sin(\angle X) = \frac{7}{10} = 0.7$$

Step3: Solve for $\angle X$

Take inverse sine: $$\angle X = \arcsin(0.7) \approx 44.4^\circ$$

Answer:

$44.4$