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nikklg [1K]
3 years ago
13

Solve for x and y please!

Mathematics
1 answer:
galina1969 [7]3 years ago
6 0

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}

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