Solve Triangle

You could simple use the Law of Sines, applying the relation of $\hat { A }$ with its opposite side and $\hat { C }$ with the hypotenuse.

$\frac{4}{\sin y} = \frac{8}{\sin 90}$

Therefore, we have that

$4 = 8 \times \sin y$

$\frac{1}{2} = \sin y$

It is easy to see that $\frac{1}{2} = \sin 30$ , so $\hat { A } =30º$ .

Now, to find $\hat { B }$ , we can use the Sum of Interior Angles of a triangle.

$\hat { A }+ \hat { B }+ \hat { C } = 180º$

$30º + \hat { B }+ 90º = 180$

$\hat { B } = 60º$

Finally, we have that $x = 60º$ and $y = 30º$ .

$\cos~x=\dfrac{4}{8}$ $\implies$ $x=\cos^{-1}\left(\dfrac{4}{8}\right)=$ $\color{#D61F06}\boxed{60}$

$\sin~y=\dfrac{4}{8}$ $\implies$ $y=\sin^{-1}\left(\dfrac{4}{8}\right)=$ $\color{#D61F06}\boxed{30}$

Easiest question so far! Since the hypotenuse is 8 units and base is 4 units in length,perpendicular is calculated to be 7.07 units via Pythagoras Theorem. Using Sine rule: Sin x =(1/8)x7.07 x=62° Therefore y=28° When rounded to nearest 10ths, x=60° y=30°