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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!
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