Answer:
[tex]\large\boxed{y\approx75.522^o\approx75.5^o}\\\\\boxed{z\approx28.956^o\approx29^o}[/tex]
Step-by-step explanation:
Look at the picture.
Use the trigonometric function
[tex]cosine=\dfrac{adjacent}{hypotenuse}[/tex]
We have:
[tex]adjacent=\dfrac{1}{2}x\\hypotenuse=2x[/tex]
Substitute:
[tex]\cos y=\dfrac{\frac{1}{2}x}{2x}=\dfrac{\frac{1}{2}}{2}=\dfrac{1}{4}\Rightarrow y\approx75.522^o[/tex]
We know: The angles in a triangle add up to 180°. Therefore:
[tex]2y+z=180^o\to2(75.522^o)+z=180^o[/tex]
[tex]151.044^o+z=180^o[/tex] subtract 151.044° from both sides
[tex]z=28.956^o[/tex]
