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Find the value of each variable

Find The Value Of Each Variable class=

Sagot :

lee08989

[tex]x = 15 \sqrt{2} [/tex]

[tex]y = 15 \sqrt{2} [/tex]

Answer:

x = y = 15[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{30}[/tex] ( multiply both sides by 30 )

30 × sin45° = x , then

x = 30 × [tex]\frac{\sqrt{2} }{2}[/tex] = 15[tex]\sqrt{2}[/tex]

The triangle is a right isosceles triangle thus the legs are congruent, then

x = y = 15[tex]\sqrt{2}[/tex]

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