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vampirchik [111]
2 years ago
10

PLEASE ANSWER AS SOON AS POSSIBLE WILL GIVE "Brainliest" TO THE FIRST CORRECT PERSON!!!

Mathematics
1 answer:
saw5 [17]2 years ago
7 0

Answer: x=18 ; y=6\sqrt{3}

Step-by-step explanation:

You can write two expressions that are in terms of 'x' and 'y'. This is a right triangle, so Pythagorean's theorem can be used. We can also use the angle to find the sine of 30 degrees.

<u>Pythagorean's Theorem:</u>

The values 'a' and 'b' are the two shorter sides of the triangle, while the value 'c' is the longest side of the triangle; the hypotenuse.

a^2+b^2=c^2

x^2+y^2=(12\sqrt{3} )^2

x^2+y^2=12^2*\sqrt{3} ^2=432

<u>Sine of the Angle:</u>

Sine is defined to be the opposite side divided by the hypotenuse. Let's take the sine of 30 degrees:

sin(\alpha )=opposite/hypotenuse

sin(30)=y/12\sqrt{3}

\frac{1}{2} =y/12\sqrt{3}

y=6\sqrt{3}

Plug this value of 'y' into the first expression derived from Pythagorean's theorem:

x^2+y^2=432

x^2+(6\sqrt{3} )^2=432

x^2+108=432

x^2=432-108=324

x=\sqrt{324}

x=18

Use this value of 'x' to solve for 'y' in the expression from Pythagorean's theorem:

(\sqrt{324})^2+y^2=432

324+y^2=432

y^2=432-324=108

y=\sqrt{108}

y=\sqrt{36*3}

y=6\sqrt{3}

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