The value of x will be equal to 33.94 units.
What is trigonometry?
Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.
Given that:-
Given that the radius of the circle is 12 units which are PO = 12 and OR = 12, QR = x , ∠O = 60 So ∠Q = 30.
First, we will calculate the Length OQ by angle property in triangle OQR.
[tex]Sin 30=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]Sin 30 = \dfrac{12}{OQ-12}[/tex]
[tex]\dfrac{1}{2}=\dfrac{12}{OQ-12}[/tex]
OQ - 12 = 24
OQ = 36
Now applying the Pythagorean theorem in the triangle OQR.
H² = P² + B²
36² = 12² + x²
x² = 1296 - 144
x = √1152
x = 33.94
Therefore the value of x will be equal to 33.94 units.
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