Question

Solve for x and y please!

Answer 1

`x = 8`

`y=2√(3)`

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√(3))^2`

Now we solve for x

`x=\sqrt{4^2 + (4√(3))^2}`

`x=√(16 +16*3)\\\\x=√(64)\\\\x=8`

Let's call z at the angle opposite to y

Then we have that:

`sin(z) =(opposite)/(hypotenuse)`

Where

`hypotenuse = 8`

`opposite=4`

`sin(z) =(4)/(8)`

`z=sin^(-1)((1)/(2))`

`z=30`

Now we use this angle to find the length y

`sin(z) =(opposite)/(hypotenuse)`

Where in this case

`hypotenuse = 4√(3)`

`opposite=y`

`z=\°30`

`sin(30\°) =(y)/(4√(3))`

`y=sin(30\°)*4√(3)`

`y=2√(3)`