Question

Find x and y.

Multiple choice answers are below!

Answer 1

Answer:

$x=8, y=8\sqrt{3}$

Step-by-step explanation:

To find y, we need to use the Law of Sines

Recall that the Law of Sines states: $\frac{a}{sin(A)} =\frac{b}{sin(B)}$

In this case, 16 is a, 90 is A, 60 is B, and y is b.

Knowing this, we can substitute in our known values, solve for y, and simplify.

$\frac{16}{sin(90)} =\frac{y}{sin(60)} \\\\y=\frac{16sin(60)}{sin(90)} \\\\y=\frac{16*\frac{\sqrt{3} }{2} }{1} ={16*\frac{\sqrt{3} }{2}=8\sqrt{2}$

Now that we know the value of two of the sides, we can use the Pythagorean Theorem to solve for x.

For simplicity, I will put the 8 back into the radical to make things easier.

$y=8\sqrt{3}=\sqrt{192}$

Recall that the Pythagorean Theorem states: $a^2+b^2=c^2$

In this case, x is a, y is b, and 16 is c.

Now we can sub in these values

$x^2+(\sqrt{192})^{2} =16^2$

Now we can solve for x and simplify

$x^2+(\sqrt{192})^{2} =16^2\\\\x^2=16^2-(\sqrt{192})^{2}\\\\x=\sqrt{16^2-(\sqrt{192})^{2}} \\\\x=\sqrt{256-192} \\\\x=\sqrt{64} \\\\x=8$