Question

Solve for x and y please!

Answer 1

Answer:

$x = 8$

$y=2\sqrt{3}$

Step-by-step explanation:

The figure is composed of 3 Right triangles. To find the values of the variables x and y we use the Pythagorean theorem to propose one equation.

$x^2 =4^2 + (4\sqrt{3})^2$

 Now we solve for x

$x=\sqrt{4^2 + (4\sqrt{3})^2}$

$x=\sqrt{16 +16*3}\\\\x=\sqrt{64}\\\\x=8$

Let's call z at the angle opposite to y

Then we have that:

$sin(z) =\frac{opposite}{hypotenuse}$

Where

$hypotenuse = 8$

$opposite=4$

$sin(z) =\frac{4}{8}$

$z=sin^{-1}(\frac{1}{2})$

$z=30$

Now we use this angle to find the length y

$sin(z) =\frac{opposite}{hypotenuse}$

Where in this case

$hypotenuse = 4\sqrt{3}$

$opposite=y$

$z=\°30$

$sin(30\°) =\frac{y}{4\sqrt{3}}$

$y=sin(30\°)*4\sqrt{3}$

$y=2\sqrt{3}$