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## Sagot :

**Answer:**

x=19, y=[tex]19\sqrt{3}[/tex]

**Step-by-step explanation:**

This triangle is a 30-60-90 triangle.

This means the hypotenuse (38) is double the short leg (x)

x=19

Then use the pythagorean theorem

a^2+b^2=c^2

19^2+y^2=38^2

361+y^2=1444

Subtract 361 from both sides

y^2=1083

put it in square roots and simplify

[tex]\sqrt{1083} =19\sqrt{3}[/tex]

y=[tex]19\sqrt{3}[/tex]

__To solve this problem__:

⇒ need to use a special right triangle theorem:

__Let's consider the information given__:

⇒ one angle is __30 degrees__

⇒ one angle marked with a little square signifies that it is __90 __

__degrees__

⇒ (all the angles added up are 180 degrees) so the last angle is

__60 degrees__

__Therefore we have a '30-60-90' triangle which states__:

- the side opposite the 30-degree angle

⇒ half the length of the hypotenuse (longest side of the triangle)

⇒ **x = 38/2 = 19**

- the side adjacent to the 30-degree angle

⇒ is the square root of 3 divided by 2 of the hypotenuse

⇒ **y = **[tex]\frac{\sqrt{3} }{2} *38=19\sqrt{3}[/tex]

__Therefore__:

**x = 19**

** **__ y = __[tex]19\sqrt{3}[/tex]

Hope that helps!